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Journal Articles Stochastics and Partial Differential Equations: Analysis and Computations Year : 2017

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

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Abstract

We 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.
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Dates and versions

hal-01192862 , version 1 (03-09-2015)

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Cite

Roland Assaraf, Benjamin Jourdain, Tony Lelièvre, Raphaël Roux. Computation of sensitivities for the invariant measure of a parameter dependent diffusion. Stochastics and Partial Differential Equations: Analysis and Computations, 2017, June 2018, 6 (2), pp.125-183. ⟨10.1007/s40072-017-0105-6⟩. ⟨hal-01192862⟩
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