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

  title={Computation of sensitivities for the invariant measure of a parameter dependent diffusion},
  author={Roland Assaraf and Benjamin Jourdain and Tony Leli{\`e}vre and Raphael Roux},
  journal={Stochastics and Partial Differential Equations: Analysis and Computations},
  • R. AssarafB. Jourdain R. Roux
  • Published 4 September 2015
  • Mathematics
  • Stochastics and Partial Differential Equations: Analysis and Computations
We consider the solution to a stochastic differential equation with a drift function which depends smoothly on some real parameter $$\lambda $$λ, and admitting a unique invariant measure for any value of $$\lambda $$λ around $$\lambda =0$$λ=0. Our aim is to compute the derivative with respect to $$\lambda $$λ of averages with respect to the invariant measure, at $$\lambda =0$$λ=0. We analyze a numerical method which consists in simulating the process at $$\lambda =0$$λ=0 together with its… 

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