Stochastic Numerics for Mathematical Physics

Stochastic Numerics for Mathematical Physics


Springer Nature Switzerland AG






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

Descrição não disponível.
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."
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
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