Weak order in averaging principle for stochastic differential equations with jumps

TL;DR

This paper investigates the averaging principle for jump-diffusion stochastic differential equations with two time scales, demonstrating that the weak convergence rate to the averaged system is of order 1, which is twice the strong convergence rate.

Contribution

It establishes the weak convergence rate for jump-diffusion SDEs with two time scales and shows it is of order 1, doubling the strong convergence rate.

Findings

Weak convergence rate is of order 1.

Weak convergence rate is twice the strong convergence rate.

Provides expansion of weak error in powers of the timescale parameter.

Abstract

The present article deals with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equation. Under suitable conditions, the weak error is expanded in powers of timescale parameter. It is proved that the rate of weak convergence to the averaged dynamics is of order $1$. This reveals the rate of weak convergence is essentially twice that of strong convergence.