Applications of the cross-entropy method to importance sampling and optimal control of diffusions
Please always quote using this URN: urn:nbn:de:0297-zib-49720
- We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.
Author: | Wei Zhang, Han Wang, Carsten HartmannORCiD, Marcus Weber, Christof Schütte |
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Document Type: | ZIB-Report |
Tag: | change of measure; cross-entropy method; important sampling; optimal control; rare events |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods |
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Exx Stochastic systems and control / 93E20 Optimal stochastic control | |
94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Axx Communication, information / 94A17 Measures of information, entropy | |
Date of first Publication: | 2014/04/23 |
Series (Serial Number): | ZIB-Report (14-10) |
ISSN: | 1438-0064 |
Published in: | Appeared in: Siam Journal on Scientific Computing 36 (2014) A 2654-A2672 |
DOI: | https://doi.org/10.1137/14096493X |