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 ${\int }_{[0,T]}f({\mu }_t,t)\circ \mathrm{d}{\mu }_t$ is well defined. For stochastic equations with this integral, we obtain the existence and uniqueness of a solution.

Stochastics: An International Journal of Probability and Stochastic Processes, 2016

References in corpus (2)

• Nonsemimartingales: Stochastic differential equations and weak Dirichlet processes
• Besov regularity of stochastic measures

Cited by in corpus (2)

• Averaging principle for equation driven by a stochastic measure
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