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Diffusion Processes And Partial Differential Equations
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Book Synopsis Diffusion Processes and Partial Differential Equations by : Kazuaki Taira
Download or read book Diffusion Processes and Partial Differential Equations written by Kazuaki Taira and published by . This book was released on 1988 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a careful and accessible exposition of functional analytic methods in stochastic analysis. It focuses on the relationship between Markov processes and elliptic boundary value problems and explores several recent developments in the theory of partial differential equations which have made further progress in the study of Markov processes possible. This book will have great appeal to both advanced students and researchers as an introduction to three interrelated subjects in analysis (Markov processes, semigroups, and elliptic boundary value problems), providing powerful methods for future research.
Book Synopsis Entropy Methods for Diffusive Partial Differential Equations by : Ansgar Jüngel
Download or read book Entropy Methods for Diffusive Partial Differential Equations written by Ansgar Jüngel and published by Springer. This book was released on 2016-06-17 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Book Synopsis Diffusion Processes and their Sample Paths by : Kiyosi Itô
Download or read book Diffusion Processes and their Sample Paths written by Kiyosi Itô and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis
Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Book Synopsis Multidimensional Diffusion Processes by : Daniel W. Stroock
Download or read book Multidimensional Diffusion Processes written by Daniel W. Stroock and published by Springer. This book was released on 2007-02-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik
Book Synopsis Stochastic Analysis and Diffusion Processes by : Gopinath Kallianpur
Download or read book Stochastic Analysis and Diffusion Processes written by Gopinath Kallianpur and published by OUP Oxford. This book was released on 2014-01-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
Book Synopsis Controlled Diffusion Processes by : N. V. Krylov
Download or read book Controlled Diffusion Processes written by N. V. Krylov and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.
Book Synopsis Partial Differential Equations and Diffusion Processes by : Russell Godding
Download or read book Partial Differential Equations and Diffusion Processes written by Russell Godding and published by . This book was released on 2018-11-22 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In probability theory and statistics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein-Uhlenbeck processes are examples of diffusion processes. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion. The position of the particle is then random; its probability density function as a function of space and time is governed by an advection-diffusion equation.
Book Synopsis Diffusion Processes and Partial Differential Equations by : Kazuaki Taira
Download or read book Diffusion Processes and Partial Differential Equations written by Kazuaki Taira and published by . This book was released on 1988 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a careful and accessible exposition of functional analytic methods in stochastic analysis. It focuses on the relationship between Markov processes and elliptic boundary value problems and explores several recent developments in the theory of partial differential equations which have made further progress in the study of Markov processes possible. This book will have great appeal to both advanced students and researchers as an introduction to three interrelated subjects in analysis (Markov processes, semigroups, and elliptic boundary value problems), providing powerful methods for future research.
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis Lectures on Diffusion Problems and Partial Differential Equations by : S. R. S. Varadhan
Download or read book Lectures on Diffusion Problems and Partial Differential Equations written by S. R. S. Varadhan and published by . This book was released on 1980 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Stochastic Modelling of Reaction–Diffusion Processes by : Radek Erban
Download or read book Stochastic Modelling of Reaction–Diffusion Processes written by Radek Erban and published by Cambridge University Press. This book was released on 2020-01-30 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
Book Synopsis Markov Processes and Differential Equations by : Mark I. Freidlin
Download or read book Markov Processes and Differential Equations written by Mark I. Freidlin and published by Birkhäuser. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Programming for Computations - MATLAB/Octave by : Svein Linge
Download or read book Programming for Computations - MATLAB/Octave written by Svein Linge and published by Springer. This book was released on 2016-08-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
Book Synopsis Diffusions and Elliptic Operators by : Richard F. Bass
Download or read book Diffusions and Elliptic Operators written by Richard F. Bass and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.
Book Synopsis Stochastic Flows and Jump-Diffusions by : Hiroshi Kunita
Download or read book Stochastic Flows and Jump-Diffusions written by Hiroshi Kunita and published by Springer. This book was released on 2019-03-26 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.
