Stochastic Numerics For Mathematical Physics

Author : Grigori N. Milstein,Michael V. Tretyakov
Publisher : Springer Nature
Page : 754 pages
File Size : 53,8 Mb
Release : 2021-12-03
Category : Computers
ISBN : 9783030820404

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

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. 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, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Author : Grigori Noah Milstein,Michael V Tretyakov
Publisher : Springer
Page : 620 pages
File Size : 50,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662100649

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

Author : Sergej Rjasanow,Wolfgang Wagner
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 51,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783540276890

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Stochastic Numerics for the Boltzmann Equation by Sergej Rjasanow,Wolfgang Wagner Pdf

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.

Author : Richard Bellman
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 41,9 Mb
Release : 1964
Category : Engineering mathematics
ISBN : 9780821813164

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Stochastic Processes in Mathematical Physics and Engineering by Richard Bellman Pdf

Author : A.B. Cruzeiro,J.-C. Zambrini
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201274

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Stochastic Analysis and Mathematical Physics by A.B. Cruzeiro,J.-C. Zambrini Pdf

This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.

Author : Yuri E. Gliklikh
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 45,7 Mb
Release : 2010-12-07
Category : Mathematics
ISBN : 0857291637

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Global and Stochastic Analysis with Applications to Mathematical Physics by Yuri E. Gliklikh Pdf

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

Author : Karl K. Sabelfeld,Nikolai A. Simonov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 208 pages
File Size : 50,5 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 : Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm
Publisher : Courier Dover Publications
Page : 529 pages
File Size : 47,7 Mb
Release : 2009-02-26
Category : Mathematics
ISBN : 9780486468990

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Nonstandard Methods in Stochastic Analysis and Mathematical Physics by Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm Pdf

Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.

Author : S Albeverio,P Blanchard,L Ferreira,T Hida,Y Kondratiev,R Vilela Mendes
Publisher : World Scientific
Page : 464 pages
File Size : 48,9 Mb
Release : 2000-11-24
Category : Science
ISBN : 9789814492270

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Mathematical Physics and Stochastic Analysis by S Albeverio,P Blanchard,L Ferreira,T Hida,Y Kondratiev,R Vilela Mendes Pdf

In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality. The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains. List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Bollé, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M Röckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L Vázquez, D N Kozakevich, S Jiménez, V R Vieira, P D Sacramento, R Vilela Mendes, D Volný, P Samek. Contents:Some Themes of the Scientific Work of Ludwig Streit (S Albeverio)Nonlinear Lie Algebras in Quantum Physics and Their Interest in Quantum Field Theory (J Beckers)Rigged Hilbert Space Resonances and Time Asymmetric Quantum Mechanics (A Bohm & H Kaldass)The Relativistic Aharonov-Bohm-Coulomb Problem: A Path Integral Solution (J Bornales et al.)Time Dependent and Nonlinear Point Interactions (R Figari)Stochastic Processes and the Feynman Integral (Z Haba)Nonrenormalizability and Nontriviality (J R Klauder)On the Spectrum of Lattice Dirac Operators (C B Lang)External and Internal Geometry on Configuration Spaces (J L Silva)Spinor Description of a General Spin-J System (V R Vieira & P D Sacramento)and other papers Readership: Theoretical physicists, mathematical physicists, mathematicians, computer scientists and economists. Keywords:

Author : Robert C. Dalang,Marco Dozzi,Franco Flandoli,Francesco Russo
Publisher : Birkhäuser
Page : 393 pages
File Size : 45,6 Mb
Release : 2015-07-28
Category : Mathematics
ISBN : 9783034809092

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Stochastic Analysis: A Series of Lectures by Robert C. Dalang,Marco Dozzi,Franco Flandoli,Francesco Russo Pdf

This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics. Contributors: S. Albeverio M. Arnaudon V. Bally V. Barbu H. Bessaih Z. Brzeźniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondreját S. Peszat M. Veraar L. Weis J.-C. Zambrini

Author : Raúl Toral,Pere Colet
Publisher : John Wiley & Sons
Page : 416 pages
File Size : 53,9 Mb
Release : 2014-06-26
Category : Science
ISBN : 9783527683123

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Stochastic Numerical Methods by Raúl Toral,Pere Colet Pdf

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations

Author : Karl K. Sabel'fel'd,Nikolai A. Simonov
Publisher : Unknown
Page : 128 pages
File Size : 44,5 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 : Gerard Ben Arous
Publisher : World Scientific
Page : 158 pages
File Size : 46,8 Mb
Release : 2008
Category : Science
ISBN : 9789812791542

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Stochastic Analysis in Mathematical Physics by Gerard Ben Arous Pdf

The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills theory and spin-glass theory.The proper concept of stochastic dynamics relevant to each type of application is described in detail here. Altogether, these approaches illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come.

Author : K. Sobczyk
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 52,7 Mb
Release : 2001-11-30
Category : Mathematics
ISBN : 1402003455

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Stochastic Differential Equations by K. Sobczyk Pdf

'Et moi, .. si lavait su CO.llUlJalt en revc: nir, One acMcc matbcmatica bu JaIdcred the human rac: c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl !be IbcII _t to !be dusty cauialcr Iabc&d 'diMardod__ The series is divergent; thc: reforc we may be -'. I!.ticT. Bc: I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non- linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...-; 'One service logic has rendered c0m- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc: hes. It also happens, quite often in fact, that branches which were thought to be completely.

Author : Sergey S. Stepanov
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 54,5 Mb
Release : 2013-06-19
Category : Mathematics
ISBN : 9783319000718

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Stochastic World by Sergey S. Stepanov Pdf

This book is an introduction into stochastic processes for physicists, biologists and financial analysts. Using an informal approach, all the necessary mathematical tools and techniques are covered, including the stochastic differential equations, mean values, probability distribution functions, stochastic integration and numerical modeling. Numerous examples of practical applications of the stochastic mathematics are considered in detail, ranging from physics to the financial theory. A reader with basic knowledge of the probability theory should have no difficulty in accessing the book content.