Stratonovich-type integral with respect to a general stochastic measure

Abstract

Let $\mu$ be a general stochastic measure, where we assume for $\mu$ only $\sigma$-additivity in probability and continuity of paths. We prove that the symmetric integral $\int_{[0,T]}f(\mu_t, t)\circ\,{\rm d}\mu_t$ is well defined. For stochastic equations with this integral, we obtain the existence and uniqueness of a solution.