Strong convergence rate of principle of averaging for jump-diffusion processes

Abstract

We study jump-diffusion processes with two well-separated time scales. It is proved that the rate of strong convergence to the averaged effective dynamics is of order O(ɛ^1/2), where ɛ ≪ 1 is the parameter measuring the disparity of the time scales in the system. The convergence rate is shown to be optimal through examples. The result sheds light on the designing of efficient numerical methods for multiscale stochastic dynamics.

Keywords

Stochastic differential equation / time scale separation / averaging of perturbations

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