Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Journal article, 2013

We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler-Maruyama discretization in time yields mean square convergence of order one in space and of order 1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mesh. © 2012 Springer Science + Business Media B.V.

Stochastic Finite Element Methods

Stochastic partial differential equations

Multilevel Monte Carlo

Stochastic parabolic equation

Multilevel approximations

Author

A. Barth

Ch. Schwab

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. 53 1 3-27

Subject Categories

Computational Mathematics

Probability Theory and Statistics

DOI

10.1007/s10543-012-0401-5

More information

Created

10/10/2017