Asymptotic Analysis for Functional Stochastic Differential Equations

Asymptotic Analysis for Functional Stochastic Differential Equations PDF Author: Jianhai Bao
Publisher: Springer
ISBN: 3319469797
Category : Mathematics
Languages : en
Pages : 159

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Book Description
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.

Asymptotic Analysis for Functional Stochastic Differential Equations

Asymptotic Analysis for Functional Stochastic Differential Equations PDF Author: Jianhai Bao
Publisher: Springer
ISBN: 3319469797
Category : Mathematics
Languages : en
Pages : 159

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Book Description
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.

Asymptotic Analysis of Differential Equations

Asymptotic Analysis of Differential Equations PDF Author: R. B. White
Publisher: World Scientific
ISBN: 1848166079
Category : Mathematics
Languages : en
Pages : 430

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Book Description
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

Asymptotic Integration of Differential and Difference Equations

Asymptotic Integration of Differential and Difference Equations PDF Author: Sigrun Bodine
Publisher: Springer
ISBN: 331918248X
Category : Mathematics
Languages : en
Pages : 411

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Book Description
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations PDF Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327

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Book Description
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Stochastic Functional Differential Equations

Stochastic Functional Differential Equations PDF Author: S. E. A. Mohammed
Publisher: Pitman Advanced Publishing Program
ISBN:
Category : Mathematics
Languages : en
Pages : 268

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Book Description


An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations PDF Author: Lawrence C. Evans
Publisher: American Mathematical Soc.
ISBN: 1470410540
Category : Mathematics
Languages : en
Pages : 161

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Book Description
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).

Stochastic Differential Equations with Markovian Switching

Stochastic Differential Equations with Markovian Switching PDF Author: Xuerong Mao
Publisher: Imperial College Press
ISBN: 1860947018
Category : Mathematics
Languages : en
Pages : 430

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Book Description
This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations PDF Author: Grigorij Kulinich
Publisher: Springer Nature
ISBN: 3030412911
Category : Mathematics
Languages : en
Pages : 249

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Book Description
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.

Parameter Estimation in Stochastic Differential Equations

Parameter Estimation in Stochastic Differential Equations PDF Author: Jaya P. N. Bishwal
Publisher: Springer
ISBN: 3540744487
Category : Mathematics
Languages : en
Pages : 271

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Book Description
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Functional Analysis for Probability and Stochastic Processes

Functional Analysis for Probability and Stochastic Processes PDF Author: Adam Bobrowski
Publisher: Cambridge University Press
ISBN: 9780521831666
Category : Mathematics
Languages : en
Pages : 416

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Book Description
This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.