Asymptotic Analysis Of Unstable Solutions Of Stochastic Differential Equations PDF Download
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| Author | : Grigorij Kulinich |
| Publisher | : Springer Nature |
| Total Pages | : 240 |
| Release | : 2020-04-29 |
| Genre | : Mathematics |
| ISBN | : 3030412911 |
Download Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations Book in PDF, ePub and Kindle
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.
| Author | : Jianhai Bao |
| Publisher | : Springer |
| Total Pages | : 159 |
| Release | : 2016-11-19 |
| Genre | : Mathematics |
| ISBN | : 3319469797 |
Download Asymptotic Analysis for Functional Stochastic Differential Equations Book in PDF, ePub and Kindle
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.
| Author | : Anatoliy M Samoilenko |
| Publisher | : World Scientific |
| Total Pages | : 323 |
| Release | : 2011-06-07 |
| Genre | : Mathematics |
| ISBN | : 981446239X |
Download Qualitative And Asymptotic Analysis Of Differential Equations With Random Perturbations Book in PDF, ePub and Kindle
Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on 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.
| Author | : Yuri Kabanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 288 |
| Release | : 2003 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9783540653325 |
Download Two-Scale Stochastic Systems Book in PDF, ePub and Kindle
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.
| Author | : White Roscoe B |
| Publisher | : World Scientific |
| Total Pages | : 432 |
| Release | : 2010-08-16 |
| Genre | : Mathematics |
| ISBN | : 1911298593 |
Download Asymptotic Analysis Of Differential Equations (Revised Edition) Book in PDF, ePub and Kindle
The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
| Author | : A. V. Skorokhod |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 339 |
| Release | : 2009-01-07 |
| Genre | : Mathematics |
| ISBN | : 9780821846865 |
Download Asymptotic Methods in the Theory of Stochastic Differential Equations Book in PDF, ePub and Kindle
Written 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.
| Author | : Mikhail V. Fedoryuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 370 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642580165 |
Download Asymptotic Analysis Book in PDF, ePub and Kindle
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
| Author | : A. V. Skorokhod |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2009-01-07 |
| Genre | : Mathematics |
| ISBN | : 9780821898253 |
Download Asymptotic Methods in the Theory of Stochastic Differential Equations Book in PDF, ePub and Kindle
Ergodic 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
| Author | : Zeev Schuus |
| Publisher | : |
| Total Pages | : 3 |
| Release | : 1977 |
| Genre | : |
| ISBN | : |
Download Asymptotic Analysis of Stochastic Differential Equations and Their Applications in Diffusion Theory, Stability of Structures and Reliability Theory Book in PDF, ePub and Kindle
| Author | : Lamberto Cesari |
| Publisher | : Springer |
| Total Pages | : 278 |
| Release | : 2013-11-09 |
| Genre | : Mathematics |
| ISBN | : 3662403684 |
Download Asymptotic Behavior and Stability Problems in Ordinary Differential Equations Book in PDF, ePub and Kindle
In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call "qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
