[PDF] Continuous Parameter Markov Processes And Stochastic Differential Equations eBook

Author : Rabi Bhattacharya
Publisher : Springer Nature
Page : 502 pages
File Size : 17,58 MB
Release : 2023-11-16
Category : Mathematics
ISBN : 3031332962

GET BOOK

This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples. After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media.

Author : Robert B. Ash
Publisher : Academic Press
Page : 332 pages
File Size : 31,88 MB
Release : 2014-06-20
Category : Mathematics
ISBN : 1483191435

GET BOOK

Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.

Author : Mark I. Freidlin
Publisher : Birkhäuser
Page : 155 pages
File Size : 23,14 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034891911

GET BOOK

Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.

Author : Vincenzo Capasso
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 24,95 MB
Release : 2012-07-27
Category : Mathematics
ISBN : 0817683461

GET BOOK

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Author : Simo Särkkä
Publisher : Cambridge University Press
Page : 327 pages
File Size : 19,40 MB
Release : 2019-05-02
Category : Business & Economics
ISBN : 1316510085

GET BOOK

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

Author : Sigurd Assing
Publisher : Springer
Page : 146 pages
File Size : 40,50 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540697861

GET BOOK

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Author : Harold J. Kushner
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 49,56 MB
Release : 2001
Category : Language Arts & Disciplines
ISBN : 9780387951393

GET BOOK

The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.

Author : Daniel T. Gillespie
Publisher : Gulf Professional Publishing
Page : 600 pages
File Size : 37,49 MB
Release : 1992
Category : Mathematics
ISBN : 9780122839559

GET BOOK

Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.

Author : Thomas Milton Liggett
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 22,58 MB
Release : 2010
Category : Mathematics
ISBN : 0821849492

GET BOOK

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.