theory of stochastic differential equations with jumps and applications mathematical and analytical techniques with applications to engineering

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Theory Of Stochastic Differential Equations With Jumps And Applications

Author : Rong SITU
ISBN : 9780387251752
Genre : Mathematics
File Size : 41. 79 MB
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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.

Methods For Constructing Exact Solutions Of Partial Differential Equations

Author : Sergey V. Meleshko
ISBN : 0387250603
Genre : Mathematics
File Size : 63. 55 MB
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Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations

Author : Umarov Sabir
ISBN : 9789813230996
Genre : Mathematics
File Size : 35. 76 MB
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The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker–Planck–Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker–Planck–Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction. This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students. Contents: Introduction The Original Triangle: Brownian Motion, Itô Stochastic Calculus, and Fokker–Planck–Kolmogorov Equation Fractional Calculus Pseudo–Differential Operators Associated with Lévy Processes Stochastic Processes and Time-Changes Stochastic Calculus for Time-Changed Semimartingales and Its Applications to SDEs Fractional Fokker–Planck–Kolmogorov Equations Readership: Graduate students and researchers in science, engineering, economics. Keywords: Fractional Fokker-Planck Equations;Stochastic Differential Equations Driven by Time-changed Processes;Levy Processes;Fractional Brownian Motion;Inverse Stable Subordinators;Continuous Time Random Walk Approximations of Time-changed Processes;Pseudo-Differential Operators with Singular Symbols;Fractional Differential EquationsReview: Key Features: The novel theory of fractional Fokker–Planck–Kolmogorov equations and their connection with the associated stochastic differential equations driven by time-changed stochastic processes are discussed in detail The book is rich in new ideas and applications to various real world problems arising in natural science, engineering, and economics. Researchers may benefit from adapting the ideas to their own research and developing relevant theory The book contains discussions of some important open problems whose solutions make significant contributions

Numerical Solution Of Stochastic Differential Equations

Author : Peter E. Kloeden
ISBN : 9783662126165
Genre : Mathematics
File Size : 84. 95 MB
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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

The Fast Solution Of Boundary Integral Equations

Author : Sergej Rjasanow
ISBN : 9780387340425
Genre : Mathematics
File Size : 43. 28 MB
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This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

Stochastic Partial Differential Equations

Author : H. Holden
ISBN : 9781468492156
Genre : Mathematics
File Size : 22. 43 MB
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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.

Applied Stochastic Control Of Jump Diffusions

Author : Bernt Øksendal
ISBN : 9783540698265
Genre : Mathematics
File Size : 51. 88 MB
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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Stochastic Calculus

Author : Mircea Grigoriu
ISBN : 0817642420
Genre : Mathematics
File Size : 81. 25 MB
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"This self-contained text may be used for several graduate courses and as an important reference resource for applied scientists interested in analytical and numerical methods for solving stochastic problems."--BOOK JACKET.

Continuous Time Stochastic Control And Optimization With Financial Applications

Author : Huyên Pham
ISBN : 9783540895008
Genre : Mathematics
File Size : 80. 61 MB
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Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Modeling With It Stochastic Differential Equations

Author : E. Allen
ISBN : 9781402059537
Genre : Mathematics
File Size : 31. 60 MB
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This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.

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