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Computation of sensitivities for the invariant measure of a parameter dependent diffusion

By Roland Assaraf, Benjamin Jourdain, Tony Lelièvre and Raphaël Roux

Abstract

International audienceWe consider the solution to a stochastic differential equation with a drift function which depends smoothly on some real parameter λ, and admitting a unique invariant measure for any value of λ around λ = 0. Our aim is to compute the derivative with respect to λ of averages with respect to the invariant measure, at λ = 0. We analyze a numerical method which consists in simulating the process at λ = 0 together with its derivative with respect to λ on long time horizon. We give sufficient conditions implying uniform-in-time square integrability of this derivative. This allows in particular to compute efficiently the derivative with respect to λ of the mean of an observable through Monte Carlo simulations

Topics: variance reduction, Feynman-Kac formulae, invariant measure, Stochastic differential equations, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Publisher: A. Debussche; B. Rozovsky
Year: 2017
DOI identifier: 10.1007/s40072-017-0105-6
OAI identifier: oai:HAL:hal-01192862v1
Provided by: Hal-Diderot

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