Stochastic Numerics for Mathematical Physics

Stochastic Numerics for Mathematical Physics

;

Springer Nature Switzerland AG

12/2021

736

Dura

Inglês

9783030820398

Pré-lançamento - envio 15 a 20 dias após a sua edição

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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."
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Stochastic Differential Equations;SDEs;backward SDEs;computing ergodic limits;geometric integration;nonglobal Lipshitz coefficients;multi-level Monte Carlo methods;variance reduction;stochastic PDEs;stochastic Hamiltonian systems;Langevin equation;nonlinear parabolic equations;Cauchy problem;Strong and Weak Approximation for SDE;mathematical biology;financial mathematics