Stochastic Numerics For Mathematical Physics

Author : Grigori N. Milstein
Publisher : Springer Nature
ISBN 13 : 3030820408
Total Pages : 754 pages
Book Rating : 4.04/5 ( download)

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Download or read book Stochastic Numerics for Mathematical Physics written by Grigori N. Milstein and published by Springer Nature. This book was released on 2021-12-03 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 9783662100646
Total Pages : 620 pages
Book Rating : 4.49/5 ( download)

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Download or read book Stochastic Numerics for Mathematical Physics written by Grigori Noah Milstein and published by Springer. This book was released on 2014-01-15 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sergej Rjasanow
Publisher : Springer Science & Business Media
ISBN 13 : 3540276890
Total Pages : 266 pages
Book Rating : 4.90/5 ( download)

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Download or read book Stochastic Numerics for the Boltzmann Equation written by Sergej Rjasanow and published by Springer Science & Business Media. This book was released on 2005-11-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : A.B. Cruzeiro
Publisher : Springer Science & Business Media
ISBN 13 : 1461201276
Total Pages : 162 pages
Book Rating : 4.74/5 ( download)

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Download or read book Stochastic Analysis and Mathematical Physics written by A.B. Cruzeiro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : American Mathematical Society
Publisher : American Mathematical Soc.
ISBN 13 : 0821813161
Total Pages : 328 pages
Book Rating : 4.64/5 ( download)

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Download or read book Stochastic Processes in Mathematical Physics and Engineering written by American Mathematical Society and published by American Mathematical Soc.. This book was released on 1964 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Karl K. Sabelfeld
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110479451
Total Pages : 208 pages
Book Rating : 4.54/5 ( download)

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Download or read book Stochastic Methods for Boundary Value Problems written by Karl K. Sabelfeld and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-09-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Courier Dover Publications
ISBN 13 : 0486468992
Total Pages : 529 pages
Book Rating : 4.90/5 ( download)

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Download or read book Nonstandard Methods in Stochastic Analysis and Mathematical Physics written by Sergio Albeverio and published by Courier Dover Publications. This book was released on 2009-02-26 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Robert C. Dalang
Publisher : Birkhäuser
ISBN 13 : 3034809093
Total Pages : 402 pages
Book Rating : 4.92/5 ( download)

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Download or read book Stochastic Analysis: A Series of Lectures written by Robert C. Dalang and published by Birkhäuser. This book was released on 2015-07-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Peter E. Kloeden
Publisher : Springer Science & Business Media
ISBN 13 : 3662126168
Total Pages : 666 pages
Book Rating : 4.65/5 ( download)

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Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Author : S Albeverio
Publisher : World Scientific
ISBN 13 : 9814492272
Total Pages : 464 pages
Book Rating : 4.70/5 ( download)

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Download or read book Mathematical Physics and Stochastic Analysis written by S Albeverio and published by World Scientific. This book was released on 2000-11-24 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: