CS29: Computing the Invariant Distribution of Linear and Non-Linear Diffusions by Ergodic Simulation
Organizer: Gilles Pagès (Sorbonne Université)
Approximation of the invariant distribution for a class of ergodic jump diffusions
Dasha Loukianova
In this talk, we approximate the invariant distribution \(\nu\) of an ergodic Jump Diffusion driven by the sum of a Brownian motion and a Compound Poisson process with sub-Gaussian jumps. We first construct an Euler discretization scheme with decreasing time steps. This scheme is similar to those introduced by Lamberton and Pagès in \([1]\) for a Brownian diffusion and extended by Panloup in \([2]\) to a diffusion with Lévy jumps. We obtain a non-asymptotic qiasi-Gaussian concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along appropriate test functions \(f\) such that \(f-\nu(f)\) is is a coboundary of the infinitesimal generator.
Bibliography
\([1]\) Damien Lamberton and Gilles Pagés. "Recursive computation of the invariant distribution of a diffusion." Bernoulli, vol. 8, no. 3, 2002, pp. 367–405.
\([2]\) Fabien Panloup. "Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process." Ann. Appl. Probab., vol. 18, no. 2, 2008, pp. 379–426.