Analysis of multi-index Monte Carlo estimators for a Zakai SPDE

Author: 

Reisinger, C
Wang, Z

Publication Date: 

1 January 2017

Journal: 

Journal of Computational Mathematics

Last Updated: 

2020-06-22T04:34:39.287+01:00

Issue: 

2

Volume: 

36

DOI: 

10.4208/jcm.1612-m2016-0681

page: 

202-236

abstract: 

In this article, we propose a space-time Multi-Index Monte Carlo (MIMC) estimator for a onedimensional parabolic stochastic partial differential equation (SPDE) of Zakai type. We compare the complexity with the Multilevel Monte Carlo (MLMC) method of Giles and Reisinger (2012), and find, by means of Fourier analysis, that the MIMC method: (i) has suboptimal complexity of O(ε −2 | log ε| 3 ) for a root mean square error (RMSE) ε if the same spatial discretisation as in the MLMC method is used; (ii) has a better complexity of O(ε −2 | log ε|) if a carefully adapted discretisation is used; (iii) has to be adapted for non-smooth functionals. Numerical tests confirm these findings empirically.

Symplectic id: 

673922

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article