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Weak approximations of solutions of a first order hyperbolic stochastic partial differential equation

Published/Copyright: June 28, 2007
Monte Carlo Methods and Applications
From the journal Volume 13 Issue 2

The present article focuses on the use of difference methods in order to approximate the solutions of stochastic partial differential equations of Itô type, in particular hyperbolic equations. We develop the main notions of deterministic difference methods, i.e. convergence, consistency and stability for the stochastic case. We prove a stochastic version of Lax-Richtmyer theorem giving the existence of a weak convergent subsequence of the approximating scheme if the scheme is both consistent and stable.

Key Words: Stochastic partial differential equations of Itô type;; difference methods;; convergence, consistency and stability;; Lax-Richtmyer.
Published Online: 2007-06-28
Published in Print: 2007-07-20

Copyright 2007, Walter de Gruyter

Articles in the same Issue

  1. On a real-time scheme for the estimation of volatility
  2. Weak approximations of solutions of a first order hyperbolic stochastic partial differential equation
  3. Exact retrospective Monte Carlo computation of arithmetic average Asian options
https://doi.org/10.1515/mcma.2007.007
Keywords for this article
Stochastic partial differential equations of Itô type;; difference methods;; convergence, consistency and stability;; Lax-Richtmyer.

Articles in the same Issue

  1. On a real-time scheme for the estimation of volatility
  2. Weak approximations of solutions of a first order hyperbolic stochastic partial differential equation
  3. Exact retrospective Monte Carlo computation of arithmetic average Asian options
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