Stochastic Numerics for Mathematical Physics

Milstein, Grigori Noah, Tretyakov, Michael V.

Stochastic Numerics for Mathematical Physics
  • 出版商: Springer
  • 出版日期: 2021-12-04
  • 售價: $7,040
  • 貴賓價: 9.5 折 $6,688
  • 語言: 英文
  • 頁數: 720
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3030820394
  • ISBN-13: 9783030820398
  • 相關分類: 物理學 Physics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

1 Mean-square approximation for stochastic differential equations.- 2 Weak approximation for stochastic differential equations.- 3 Numerical methods for SDEs with small noise.- 4 Stochastic Hamiltonian systems and Langevin-type equations.- 5 Simulation of space and space-time bounded diffusions.- 6 Random walks for linear boundary value problems.- 7 Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations.- 8 Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach.- 9 Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets.- A Appendix: Practical guidance to implementation of the stochastic numerical methods.- A.1 Mean-square methods.- A.2 Weak methods and the Monte Carlo technique.- A.3 Algorithms for bounded diffusions.- A.4 Random walks for linear boundary value problems.- A.5 Nonlinear PDEs.- A.6 Miscellaneous.- References.
new TOC

"In the updated edition we are planning to include the following new material:

(i) numerics for backward SDEs to which a new chapter will be dedicated;

(ii) we will extend chapter 4 by new results on Geometric Integration of SDEs and computing ergodic limits (long time integration of SDEs);

(iii) we will add recent results for SDEs with nonglobal Lipshitz coefficients to Chapters 1 and 2;

(iv) we will add a new chapter or extend Chapter 2 to include multi-level Monte Carlo methods which has been developed since 2008 and new results on variance reduction.

We will also explore a possibility to include some material on stochastic PDEs. We will remove Chapter 9 and either remove or transform Chapter 8. Further, natural changes will occur during the work on the new edition."


作者簡介

Professor G.N. Milstein received his undergraduate degree in mathematics from the Ural State University (UrGU; Sverdlovsk, USSR), which is now Ural Federal University (Ekaterinburg, Russia). He completed his PhD studies at the same University. Professor Milstein has been an assistant professor, associate professor and, after defending his DSc thesis, professor at the Faculty of Mathematics and Mechanics of UrGU (then URFU). For a number of years, he worked as a senior researcher at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS; Berlin, Germany). He was also a Visiting Professor at the University of Leicester (UK) and the University of Manchester (UK). Professor Milstein has a world-leading expertise in stochastic numerics, estimation, control, stability, financial mathematics. Milstein's early pioneering papers on numerical methods for stochastic differential equations are the cornerstones of the modern stochastic numerics.Professor M.V. Tretyakov received his undergraduate degree in mathematics from the Ural State University (UrGU; Sverdlovsk, USSR). He completed his PhD studies at the same University. Professor Tretyakov has gained experience in stochastic numerics during his stay at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS, Berlin) as a DAAD Research Fellow and then a Research Fellow of the Alexander von Humboldt Foundation. He worked as senior researcher at the Institute of Mathematics and Mechanics (Russian Academy of Sciences, Ekaterinburg) and at UrGU. He was a lecturer at Swansea University (UK) and a lecturer, reader and professor at the University of Leicester (UK). Since 2012 he is a professor at the University of Nottingham (UK). He has served on editorial boards of numerical analysis and scientific computing journals. His research has been supported by the Leverhulme Trust, EPSRC, BBSRC, and Royal Society. Professor Tretyakov has extensive world-class expertise in stochastic numerical analysis. He also conducts high quality research in financial mathematics, stochastic dynamics, and uncertainty quantification.

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