Hartmann, C. and Schütte, Ch. and Weber, M. and Zhang, W. (2018) Importance sampling in path space for diffusion processes with slowfast variables. Probab. Theory Rel. Fields, 170 (12). pp. 177228. ISSN 01788051 (print) 14322064 (online)

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Official URL: https://dx.doi.org/10.1007/s0044001707553
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 zerovariance estimator and is related to the solution of a HamiltonJacobiBellmann 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:  17 Jan 2020 10:46 
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