Averaging principle for equation driven by a stochastic measure

ABSTRACT

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only σ-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.

KEYWORDS:

• Averaging principle
• symmetric integral
• stochastic measure
• stochastic ordinary differential equations
• Doss–Sussmann transformation

Acknowledgments

The author is grateful to Prof. M. Zähle for fruitful discussions during the preparation of this paper and thanks the Friedrich–Schiller–University of Jena for its hospitality.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

V. M. Radchenko  http://orcid.org/0000-0002-8234-2797

Additional information

Funding

This work was supported by Alexander von Humboldt Foundation, grant 1074615.