Stochastic Methods For Boundary Value Problems

Author : Karl K. Sabelfeld,Nikolai A. Simonov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 208 pages
File Size : 52,6 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9783110479454

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Stochastic Methods for Boundary Value Problems by Karl K. Sabelfeld,Nikolai A. Simonov Pdf

This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach. The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics. Contents: Introduction Random walk algorithms for solving integral equations Random walk-on-boundary algorithms for the Laplace equation Walk-on-boundary algorithms for the heat equation Spatial problems of elasticity Variants of the random walk on boundary for solving stationary potential problems Splitting and survival probabilities in random walk methods and applications A random WOS-based KMC method for electron–hole recombinations Monte Carlo methods for computing macromolecules properties and solving related problems Bibliography

Author : Karl K. Sabel'fel'd,Nikolai A. Simonov
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 2016
Category : Electronic
ISBN : 311047946X

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Stochastic Methods for Boundary Value Problems by Karl K. Sabel'fel'd,Nikolai A. Simonov Pdf

Author : Kazuaki Taira
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 49,8 Mb
Release : 2009-06-30
Category : Mathematics
ISBN : 9783642016769

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Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

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 : G. S. Ladde,M. Sambandham
Publisher : CRC Press
Page : 269 pages
File Size : 54,9 Mb
Release : 2003-12-05
Category : Mathematics
ISBN : 9780203027028

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Stochastic versus Deterministic Systems of Differential Equations by G. S. Ladde,M. Sambandham Pdf

This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its met

Author : Kai Lai Chung
Publisher : World Scientific Publishing Company
Page : 180 pages
File Size : 41,8 Mb
Release : 2002-05-06
Category : Mathematics
ISBN : 9789813102521

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Green, Brown, and Probability and Brownian Motion on the Line by Kai Lai Chung Pdf

This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity — Green's formula for solving the boundary value problem of Laplace equations and the Newton–Coulomb potential. Part II of the book comprises lecture notes based on a short course on “Brownian Motion on the Line” which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.

Author : Dongxiao Zhang
Publisher : Elsevier
Page : 371 pages
File Size : 54,7 Mb
Release : 2001-10-11
Category : Mathematics
ISBN : 9780080517773

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Stochastic Methods for Flow in Porous Media by Dongxiao Zhang Pdf

Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes Practical examples throughout the text Exercises at the end of each chapter reinforce specific concepts and techniques For the reader who is interested in hands-on experience, a number of computer codes are included and discussed

Author : Kazuaki Taira
Publisher : Unknown
Page : 502 pages
File Size : 42,9 Mb
Release : 2020
Category : Boundary value problems
ISBN : 303048789X

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Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.

Author : Goran Peskir,Albert Shiryaev
Publisher : Springer Science & Business Media
Page : 515 pages
File Size : 55,6 Mb
Release : 2006-11-10
Category : Mathematics
ISBN : 9783764373900

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Optimal Stopping and Free-Boundary Problems by Goran Peskir,Albert Shiryaev Pdf

This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

Author : Karl Karlovich Sabelʹfelʹd
Publisher : Springer
Page : 314 pages
File Size : 45,8 Mb
Release : 1991-10-04
Category : Language Arts & Disciplines
ISBN : UCAL:B4359705

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Monte Carlo Methods by Karl Karlovich Sabelʹfelʹd Pdf

This book deals with Random Walk Methods for solving multidimensional boundary value problems. Monte Carlo algorithms are constructed for three classes of problems: (1) potential theory, (2) elasticity, and (3) diffusion. Some of the advantages of our new methods as compared to conventional numerical methods are that they cater for stochasticities in the boundary value problems and complicated shapes of the boundaries.

Author : Guy Fayolle,Roudolf Iasnogorodski,Vadim Malyshev
Publisher : Springer Science & Business Media
Page : 169 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642600012

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Random Walks in the Quarter-Plane by Guy Fayolle,Roudolf Iasnogorodski,Vadim Malyshev Pdf

Promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries, the authors use Using Riemann surfaces and boundary value problems to propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.

Author : Franco Flandoli
Publisher : CRC Press
Page : 94 pages
File Size : 47,5 Mb
Release : 1995-08-03
Category : Science
ISBN : 2884490450

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Regularity Theory and Stochastic Flows for Parabolic \ISPDES\n by Franco Flandoli Pdf

First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Stefan A. Sauter,Christoph Schwab
Publisher : Springer Science & Business Media
Page : 575 pages
File Size : 54,8 Mb
Release : 2010-11-01
Category : Mathematics
ISBN : 9783540680932

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Boundary Element Methods by Stefan A. Sauter,Christoph Schwab Pdf

This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in $\mathbb{R}^3$. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of Galerkin boundary element methods, which is one of the most flexible and robust numerical discretization methods for integral equations. For the efficient realization of the Galerkin BEM, it is essential to replace time-consuming steps in the numerical solution process with fast algorithms. In Chapters 5-9 these methods are developed, analyzed, and formulated in an algorithmic way.

Author : Kazuaki Taira
Publisher : Springer
Page : 724 pages
File Size : 42,9 Mb
Release : 2014-08-07
Category : Mathematics
ISBN : 9783662436967

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Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.

Author : Grigori Noah Milstein,Michael V. Tretyakov
Publisher : Springer Science & Business Media
Page : 612 pages
File Size : 49,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662100639

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Stochastic Numerics for Mathematical Physics by Grigori Noah Milstein,Michael V. Tretyakov Pdf

Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Author : Dmitry G. Arseniev,Vladimir M. Ivanov,Maxim L. Korenevsky
Publisher : Walter de Gruyter GmbH & Co KG
Page : 290 pages
File Size : 49,5 Mb
Release : 2018-01-09
Category : Mathematics
ISBN : 9783110553673

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Adaptive Stochastic Methods by Dmitry G. Arseniev,Vladimir M. Ivanov,Maxim L. Korenevsky Pdf

This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics. Contents Part I: Evaluation of Integrals Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals Sequential Monte Carlo Method and Adaptive Integration Methods of Adaptive Integration Based on Piecewise Approximation Methods of Adaptive Integration Based on Global Approximation Numerical Experiments Adaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral Equations Semi-Statistical Method of Solving Integral Equations Numerically Problem of Vibration Conductivity Problem on Ideal-Fluid Flow Around an Airfoil First Basic Problem of Elasticity Theory Second Basic Problem of Elasticity Theory Projectional and Statistical Method of Solving Integral Equations Numerically