Download or read book Analytic Approximations of Solutions to Stochastic Differential Equations written by Svetlana Janković and published by . This book was released on 2008 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. 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
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Stochastic Analysis written by Shigeo Kusuoka and published by Springer Nature. This book was released on 2020-10-20 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations.
Download or read book Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations written by Grigorij Kulinich and published by Springer Nature. This book was released on 2020-04-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.
Download or read book Stochastic Differential and Difference Equations written by Imre Csiszár and published by Springer Science & Business Media. This book was released on 1997 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Periodically Correlated Solutions to a Class of Stochastic Difference Equations.- On Nonlinear SDE'S whose Densities Evolve in a Finite-Dimensional Family.- Composition of Skeletons and Support Theorems.- Invariant Measure for a Wave Equation on a Riemannian Manifold.- Ergodic Distributed Control for Parameter Dependent Stochastic Semilinear Systems.- Dirichlet Forms, Caccioppoli Sets and the Skorohod Equation Masatoshi Fukushima.- Rate of Convergence of Moments of Spall's SPSA Method.- General Setting for Stochastic Processes Associated with Quantum Fields.- On a Class of Semilinear Stochastic Partial Differential Equations.- Parallel Numerical Solution of a Class of Volterra Integro-Differential Equations.- On the Laws of the Oseledets Spaces of Linear Stochastic Differential Equations.- On Stationarity of Additive Bilinear State-space Representation of Time Series.- On Convergence of Approximations of Ito-Volterra Equations.- Non-isotropic Ornstein-Uhlenbeck Process and White Noise Analysis.- Stochastic Processes with Independent Increments on a Lie Group and their Selfsimilar Properties.- Optimal Damping of Forced Oscillations Discrete-time Systems by Output Feedback.- Forecast of Lévy's Brownian Motion as the Observation Domain Undergoes Deformation.- A Maximal Inequality for the Skorohod Integral.- On the Kinematics of Stochastic Mechanics.- Stochastic Equations in Formal Mappings.- On Fisher's Information Matrix of an ARMA Process.- Statistical Analysis of Nonlinear and NonGaussian Time Series.- Bilinear Stochastic Systems with Long Range Dependence in Continuous Time.- On Support Theorems for Stochastic Nonlinear Partial Differential Equations.- Excitation and Performance in Continuous-time Stochastic Adaptive LQ-control.- Invariant Measures for Diffusion Processes in Conuclear Spaces.- Degree Theory on Wiener Space and an Application to a Class of SPDEs.- On the Interacting Measure-Valued Branching Processes.
Download or read book Stochastic Partial Differential Equations written by Helge Holden and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.
Download or read book Introduction to Stochastic Analysis written by Vigirdas Mackevicius and published by John Wiley & Sons. This book was released on 2013-02-07 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.
Download or read book Approximations of Solutions of Stochastic Differential Equations written by Janusz Staniskaw Golec and published by . This book was released on 1988 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction To Differential Equations An Stochastic Modeling Methods And Analysis Volume 2 written by Anilchandra G Ladde and published by World Scientific Publishing Company. This book was released on 2013-01-11 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)
Download or read book Theory of Stochastic Differential Equations with Jumps and Applications written by Rong SITU and published by Springer Science & Business Media. This book was released on 2006-05-06 with total page 444 pages. Available in PDF, EPUB and Kindle. 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.
Download or read book Two Scale Stochastic Systems written by Yuri Kabanov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.
Download or read book Trotter Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications written by T. E. Govindan and published by Springer Nature. This book was released on with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Stochastic Differential Equations written by Lawrence C. Evans and published by American Mathematical Soc.. This book was released on 2012-12-11 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).
Download or read book An Introduction to the Numerical Simulation of Stochastic Di erential Equations written by Desmond J. Higham and published by SIAM. This book was released on 2021-01-28 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks. Although introductory, the book covers a range of modern research topics, including Itô versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks. An Introduction to the Numerical Simulation of Stochastic Differential Equations is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.
Download or read book Stochastic Integral And Differential Equations In Mathematical Modelling written by Santanu Saha Ray and published by World Scientific. This book was released on 2023-04-25 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes — either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
