Asymptotic Methods in the Theory of Stochastic Differential Equations
Author: Anatoliĭ Vladimirovich Skorokhod
Publisher: Amer Mathematical Society
Published: 1989
Total Pages: 339
ISBN-13: 9780821845318
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Asymptotic Methods in the Theory of Stochastic Differential Equations
Author: A. V. Skorokhod
Publisher: American Mathematical Soc.
Published: 2009-01-07
Total Pages: 339
ISBN-13: 9780821846865
DOWNLOAD EBOOKWritten by one of the foremost Soviet experts in the field, this book is intended for specialists in the theory of random processes and its applications. The author's 1982 monograph on stochastic differential equations, written with Iosif Ilich Gikhman, did not include a number of topics important to applications. The present work begins to fill this gap by investigating the asymptotic behavior of stochastic differential equations. The main topics are ergodic theory for Markov processes and for solutions of stochastic differential equations, stochastic differential equations containing a small parameter, and stability theory for solutions of systems of stochastic differential equations.
Asymptotic Methods in the Theory of Stochastic Differential Equations
Author: A. V. Skorokhod
Publisher: American Mathematical Soc.
Published: 2009-01-07
Total Pages: 362
ISBN-13: 9780821898253
DOWNLOAD EBOOKErgodic theorems: General ergodic theorems Densities for transition probabilities and resolvents for Markov solutions of stochastic differential equations Ergodic theorems for one-dimensional stochastic equations Ergodic theorems for solutions of stochastic equations in $R^d$ Asymptotic behavior of systems of stochastic equations containing a small parameter: Equations with a small right-hand side Processes with rapid switching Averaging over variables for systems of stochastic differential equations Stability. Linear systems: Stability of sample paths of homogeneous Markov processes Linear equations in $R^d$ and the stochastic semigroups connected with them. Stability Stability of solutions of stochastic differential equations Linear stochastic equations in Hilbert space. Stochastic semigroups. Stability: Linear equations with bounded coefficients Strong stochastic semigroups with second moments Stability Bibliography
Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
Author: Grigorij Kulinich
Publisher: Springer Nature
Published: 2020-04-29
Total Pages: 240
ISBN-13: 3030412911
DOWNLOAD EBOOKThis 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.
Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations
Author: Anatoli? Mikha?lovich Samo?lenko
Publisher: World Scientific
Published: 2011
Total Pages: 323
ISBN-13: 9814329061
DOWNLOAD EBOOKDifferential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on the random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.
Asymptotic Analysis for Functional Stochastic Differential Equations
Author: Jianhai Bao
Publisher: Springer
Published: 2016-11-19
Total Pages: 159
ISBN-13: 3319469797
DOWNLOAD EBOOKThis 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 Methods in the Theory of Linear Differential Equations
Author: Stepan Fedorovich Feshchenko
Publisher:
Published: 1967
Total Pages: 298
ISBN-13:
DOWNLOAD EBOOKAsymptotic Integration of Differential and Difference Equations
Author: Sigrun Bodine
Publisher: Springer
Published: 2015-05-26
Total Pages: 411
ISBN-13: 331918248X
DOWNLOAD EBOOKThis 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.
Introduction to Asymptotic Methods
Author: David Y. Gao
Publisher: CRC Press
Published: 2006-05-03
Total Pages: 270
ISBN-13: 1420011731
DOWNLOAD EBOOKAmong the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Statistical Methods for Stochastic Differential Equations
Author: Mathieu Kessler
Publisher: CRC Press
Published: 2012-05-17
Total Pages: 507
ISBN-13: 1439849765
DOWNLOAD EBOOKThe seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to th
