Repository: Freie Universität Berlin, Math Department

Importance sampling in path space for diffusion processes with slow-fast variables

Hartmann, C. and Schütte, Ch. and Weber, M. and Zhang, W. (2017) Importance sampling in path space for diffusion processes with slow-fast variables. Probab. Theory Rel. Fields, 170 (1-2). pp. 177-228. ISSN 1432-2064 (online)

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Official URL: https://link.springer.com/article/10.1007%2Fs00440...

Abstract

Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton-Jacobi-Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with a simple numerical example.

Item Type:Article
Additional Information:SFB 1114 Preprint 02/2015 in arXiv:1502.07899
Subjects:Mathematical and Computer Sciences > Mathematics > Mathematical Methods
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group
Other Institutes > Matheon
ID Code:1321
Deposited By: Carsten Hartmann
Deposited On:13 Sep 2013 18:58
Last Modified:26 Feb 2018 11:13

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