Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications
Author: Avner Friedman
Publsiher: Courier Corporation
Total Pages: 562
Release: 2006-12-01
ISBN: 0486453596
Category: Mathematics
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations and Applications Book Excerpt:

Originally published in 2 volumes, this text develops the theory of systems of stochastic differential equations and presents applications in probability, partial differential equations, and stochastic control problems. 1975 edition.

Stochastic Differential Equations and Applications

Stochastic Differential Equations and Applications
Author: X Mao
Publsiher: Elsevier
Total Pages: 440
Release: 2007-12-30
ISBN: 085709940X
Category: Mathematics
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations and Applications Book Excerpt:

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systems Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists

Stochastic Differential Equations

Stochastic Differential Equations
Author: Bernt Øksendal
Publsiher: Springer Science & Business Media
Total Pages: 406
Release: 2003
ISBN: 3540047581
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations Book Excerpt:

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010.

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance
Author: Carlos A. Braumann
Publsiher: John Wiley & Sons
Total Pages: 304
Release: 2019-03-08
ISBN: 1119166071
Category: Mathematics
Language: EN, FR, DE, ES & NL

Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance Book Excerpt:

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential Equations with Applications
Author: Kai Liu
Publsiher: CRC Press
Total Pages: 312
Release: 2005-08-23
ISBN: 1420034820
Category: Mathematics
Language: EN, FR, DE, ES & NL

Stability of Infinite Dimensional Stochastic Differential Equations with Applications Book Excerpt:

Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ

Forward Backward Stochastic Differential Equations and their Applications

Forward Backward Stochastic Differential Equations and their Applications
Author: Jin Ma,Jiongmin Yong
Publsiher: Springer
Total Pages: 278
Release: 2007-04-24
ISBN: 3540488316
Category: Mathematics
Language: EN, FR, DE, ES & NL

Forward Backward Stochastic Differential Equations and their Applications Book Excerpt:

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Stochastic Differential Equations

Stochastic Differential Equations
Author: K. Sobczyk
Publsiher: Springer Science & Business Media
Total Pages: 428
Release: 2001-11-30
ISBN: 9781402003455
Category: Mathematics
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations Book Excerpt:

'Et moi, ..~ si lavait su CO.llUlJalt en revc:nir, One acMcc matbcmatica bu JaIdcred the human rac:c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl !be~ IbcII _t to !be dusty cauialcr Iabc&d 'diMardod__ The series is divergent; thc:reforc we may be -'. I!.ticT. Bc:I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non­ linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...•; 'One service logic has rendered c0m­ puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc:hes. It also happens, quite often in fact, that branches which were thought to be completely.

Stochastic Differential Equations

Stochastic Differential Equations
Author: Ludwig Arnold
Publsiher: Wiley-Interscience
Total Pages: 252
Release: 1974-04-23
ISBN: 1928374650XXX
Category: Mathematics
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations Book Excerpt:

Fundamentals of probability theory; Markov processes and diffusion processes; Wiener process and white noise; Stochastic integrals; The stochastic integral as a stochastic process, stochastic differentials; Stochastic differential equations, existence and uniqueness of solutions; Properties of the solutions of stochastic differential equations; Linear stochastic differentials equations; The solutions of stochastic differentail equations as Markov and diffusion processes; Questions of modeling and approximation; Stability of stochastic dynamic systems; Optimal filtering of a disturbed signal; Optimal control of stochastic dynamic systems.

Reflecting Stochastic Differential Equations with Jumps and Applications

Reflecting Stochastic Differential Equations with Jumps and Applications
Author: Situ Rong
Publsiher: CRC Press
Total Pages: 228
Release: 1999-08-05
ISBN: 9781584881254
Category: Mathematics
Language: EN, FR, DE, ES & NL

Reflecting Stochastic Differential Equations with Jumps and Applications Book Excerpt:

Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.

Stochastic Partial Differential Equations and Applications

Stochastic Partial Differential Equations and Applications
Author: Giuseppe Da Prato,Luciano Tubaro
Publsiher: Lecture Notes in Mathematics
Total Pages: 274
Release: 1987-03-25
ISBN: 1928374650XXX
Category: Mathematics
Language: EN, FR, DE, ES & NL

Stochastic Partial Differential Equations and Applications Book Excerpt:

Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.

Numerical Solution of Stochastic Differential Equations

Numerical Solution of Stochastic Differential Equations
Author: Peter E. Kloeden,Eckhard Platen
Publsiher: Springer Science & Business Media
Total Pages: 636
Release: 2013-04-17
ISBN: 3662126168
Category: Mathematics
Language: EN, FR, DE, ES & NL

Numerical Solution of Stochastic Differential Equations Book Excerpt:

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Theory and Applications of Stochastic Differential Equations

Theory and Applications of Stochastic Differential Equations
Author: Zeev Schuss
Publsiher: John Wiley & Sons Incorporated
Total Pages: 342
Release: 1980
ISBN: 1928374650XXX
Category: Mathematics
Language: EN, FR, DE, ES & NL

Theory and Applications of Stochastic Differential Equations Book Excerpt:

Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists.

Theory of Stochastic Differential Equations with Jumps and Applications

Theory of Stochastic Differential Equations with Jumps and Applications
Author: Rong SITU
Publsiher: Springer Science & Business Media
Total Pages: 458
Release: 2005-04-20
ISBN: 9780387250830
Category: Mathematics
Language: EN, FR, DE, ES & NL

Theory of Stochastic Differential Equations with Jumps and Applications Book Excerpt:

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications
Author: Łukasz Delong
Publsiher: Springer Science & Business Media
Total Pages: 288
Release: 2013-06-12
ISBN: 1447153316
Category: Mathematics
Language: EN, FR, DE, ES & NL

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications Book Excerpt:

Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.

Delay Differential Equations and Applications to Biology

Delay Differential Equations and Applications to Biology
Author: Fathalla A. Rihan
Publsiher: Springer Nature
Total Pages: 286
Release: 2021-08-19
ISBN: 9811606269
Category: Mathematics
Language: EN, FR, DE, ES & NL

Delay Differential Equations and Applications to Biology Book Excerpt:

This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.

Stochastic Differential Equations An Introduction With Applications 6E

Stochastic Differential Equations  An Introduction With Applications  6E
Author: Bernt K. Øksendal,Oksendal Bernt
Publsiher: Unknown
Total Pages: 388
Release: 2003
ISBN: 9788181281531
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations An Introduction With Applications 6E Book Excerpt:

Stochastic Differential Equations

Stochastic Differential Equations
Author: Peter H. Baxendale,Sergey V. Lototsky
Publsiher: World Scientific
Total Pages: 416
Release: 2007
ISBN: 9812706623
Category: Science
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations Book Excerpt:

The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.

Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
Author: T. E. Govindan
Publsiher: Springer
Total Pages: 407
Release: 2016-11-11
ISBN: 3319456849
Category: Mathematics
Language: EN, FR, DE, ES & NL

Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications Book Excerpt:

This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.

Stochastic Methods and their Applications to Communications

Stochastic Methods and their Applications to Communications
Author: Serguei Primak,Valeri Kontorovich,Vladimir Lyandres
Publsiher: John Wiley & Sons
Total Pages: 446
Release: 2005-01-28
ISBN: 0470021179
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Stochastic Methods and their Applications to Communications Book Excerpt:

Stochastic Methods & their Applications to Communications presents a valuable approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. The authors provide a detailed account of random processes from an engineering point of view and illustrate the concepts with examples taken from the communications area. The discussions mainly focus on the analysis and synthesis of Markov models of random processes as applied to modelling such phenomena as interference and fading in communications. Encompassing both theory and practice, this original text provides a unified approach to the analysis and generation of continuous, impulsive and mixed random processes based on the Fokker-Planck equation for Markov processes. Presents the cumulated analysis of Markov processes Offers a SDE (Stochastic Differential Equations) approach to the generation of random processes with specified characteristics Includes the modelling of communication channels and interfer ences using SDE Features new results and techniques for the of solution of the generalized Fokker-Planck equation Essential reading for researchers, engineers, and graduate and upper year undergraduate students in the field of communications, signal processing, control, physics and other areas of science, this reference will have wide ranging appeal.

Stochastic Differential Equations Theory and Applications

Stochastic Differential Equations  Theory and Applications
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 2022
ISBN: 9814475424
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Stochastic Differential Equations Theory and Applications Book Excerpt: