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Theory Of Stochastic Differential Equations With Jumps And Applications

Author: Rong SITU
Publisher: Springer Science & Business Media
ISBN: 0387251758
Size: 79.68 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.

Asymptotic Analysis For Functional Stochastic Differential Equations

Author: Jianhai Bao
Publisher: Springer
ISBN: 3319469797
Size: 39.86 MB
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This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Methods For Constructing Exact Solutions Of Partial Differential Equations

Author: Sergey V. Meleshko
Publisher: Springer Science & Business Media
ISBN: 9780387250601
Size: 46.66 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
Publisher: World Scientific
ISBN: 9813230991
Size: 26.87 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

Stochastic Calculus

Author: Mircea Grigoriu
Publisher: Springer Science & Business Media
ISBN: 9780817642426
Size: 12.95 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.

Mathematical Methods In Robust Control Of Linear Stochastic Systems

Author: Vasile Dragan
Publisher: Springer Science & Business Media
ISBN: 1461486637
Size: 72.34 MB
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This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. More specifically, the new results presented are: - A unified and abstract framework for Riccati type equations arising in the stochastic control - Stability and control problems for systems perturbed by homogeneous Markov processes with infinite number of states - Mixed H2 / H∞ control problem and numerical procedures - Linear differential equations with positive evolution on ordered Banach spaces with applications for stochastic systems including both multiplicative white noise and Markovian jumps represented by a Markov chain with countable infinite set of states - Kalman filtering for stochastic systems subject both to state dependent noise and Markovian jumps - H∞ reduced order filters for stochastic systems The book will appeal to graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis. From Reviews of the First Edition: This book is concerned with robust control of stochastic systems. One of the main features is its coverage of jump Markovian systems. ... Overall, this book presents results taking into consideration both white noise and Markov chain perturbations. It is clearly written and should be useful for people working in applied mathematics and in control and systems theory. The references cited provide further reading sources. (George Yin, Mathematical Reviews, Issue 2007 m) This book considers linear time varying stochastic systems, subjected to white noise disturbances and system parameter Markovian jumping, in the context of optimal control ... robust stabilization, and disturbance attenuation. ... The material presented in the book is organized in seven chapters. ... The book is very well written and organized. ... is a valuable reference for all researchers and graduate students in applied mathematics and control engineering interested in linear stochastic time varying control systems with Markovian parameter jumping and white noise disturbances. (Zoran Gajic, SIAM Review, Vol. 49 (3), 2007)

Stochastic Dynamics

Author: Hans Crauel
Publisher: Springer Science & Business Media
ISBN: 0387226559
Size: 68.17 MB
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Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.