# Averaging principle for equation driven by a stochastic measure

## TL;DR

This paper establishes an averaging principle for equations driven by a stochastic measure with symmetric integral, proving convergence and estimating the rate, under minimal assumptions on the integrator.

## Contribution

It extends the averaging principle to equations driven by stochastic measures with only $\sigma$-additivity and path continuity assumptions.

## Key findings

- Averaging principle holds under minimal assumptions.
- Convergence rate to the averaged solution is estimated.
- Applicable to equations with symmetric stochastic integrals.

## Abstract

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for this case, the rate of convergence to the solution of the averaged equation is estimated.