Markov Processes And Differential Equations PDF Download
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Author | : Mark I. Freidlin |
Publisher | : Birkhäuser |
Total Pages | : 155 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034891911 |
Download Markov Processes and Differential Equations Book in PDF, ePub and Kindle
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 | : Rabi Bhattacharya |
Publisher | : Springer Nature |
Total Pages | : 502 |
Release | : 2023-11-16 |
Genre | : Mathematics |
ISBN | : 3031332962 |
Download Continuous Parameter Markov Processes and Stochastic Differential Equations Book in PDF, ePub and Kindle
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 | : Avner Friedman |
Publisher | : Academic Press |
Total Pages | : 248 |
Release | : 2014-06-20 |
Genre | : Mathematics |
ISBN | : 1483217876 |
Download Stochastic Differential Equations and Applications Book in PDF, ePub and Kindle
Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov’s formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.
Author | : Wendell H. Fleming |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2006-02-04 |
Genre | : Mathematics |
ISBN | : 0387310711 |
Download Controlled Markov Processes and Viscosity Solutions Book in PDF, ePub and Kindle
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Author | : Daniel W. Stroock |
Publisher | : Princeton University Press |
Total Pages | : 289 |
Release | : 2003-05-06 |
Genre | : Mathematics |
ISBN | : 1400835577 |
Download Markov Processes from K. Itô's Perspective (AM-155) Book in PDF, ePub and Kindle
Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.
Author | : J. A. van Casteren |
Publisher | : World Scientific |
Total Pages | : 825 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814322180 |
Download Markov Processes, Feller Semigroups and Evolution Equations Book in PDF, ePub and Kindle
The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.
Author | : Daniel T. Gillespie |
Publisher | : Gulf Professional Publishing |
Total Pages | : 600 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9780122839559 |
Download Markov Processes Book in PDF, ePub and Kindle
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 | : Jan A Van Casteren |
Publisher | : World Scientific |
Total Pages | : 825 |
Release | : 2010-11-25 |
Genre | : Mathematics |
ISBN | : 9814464171 |
Download Markov Processes, Feller Semigroups And Evolution Equations Book in PDF, ePub and Kindle
The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.
Author | : Kazuaki Taira |
Publisher | : Springer Science & Business Media |
Total Pages | : 196 |
Release | : 2009-06-30 |
Genre | : Mathematics |
ISBN | : 3642016766 |
Download Boundary Value Problems and Markov Processes Book in PDF, ePub and Kindle
This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
Author | : Bernt Oksendal |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662130505 |
Download Stochastic Differential Equations Book in PDF, ePub and Kindle
These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.