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Forward sensitivity analysis for contracting stochastic systems

Part of: Markov processes Numerical problems in dynamical systems

Published online by Cambridge University Press:  20 March 2018

Thomas Flynn
Thomas Flynn*
Affiliation:
City University of New York
*
* Current address: Computational Science Initiative, Brookhaven National Laboratory, P.O. Box 5000, Upton, NY 11973, USA. Email address: tflynn@bnl.gov
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Abstract

In this paper we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance, that guarantee differentiability of stationary costs. Then we show how to estimate the derivatives, deriving an estimator that can be seen as a generalization of the forward sensitivity analysis method used in deterministic systems. We apply the results to examples, including a neural network model.

Keywords

Markov chainderivative estimationcontractioniterated function system

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 90C31: Sensitivity, stability, parametric optimization 65P99: None of the above, but in this section
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 1 , March 2018 , pp. 102 - 130
Copyright
Copyright © Applied Probability Trust 2018 

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