Stochastic Volterra equation driven by Wiener process and fractional Brownian motion (Q2015764)

In this paper, a class of so-called mixed stochastic Volterra equations on \(\mathbb{R}^d\) is studied. The equations considered are driven by both a Wiener process and fractional Brownian motion. The paper is a continuation and extension of several papers published since 2002. The main result of the paper, Theorem~1, gives sufficient conditions under which the studied equations have a unique strong solution. The proof of the main theorem is based on the classical Yamada and Watanabe theorem [\textit{T. Yamada} and \textit{S. Watanabe}, J. Math. Kyoto Univ. 11, 155--167 (1971; Zbl 0236.60037); ibid. 11, 553--563 (1971; Zbl 0229.60039)]. The proof of Theorem~1 is clearly written in detail. Moreover, the authors derive several auxiliary estimates for the integrals involved in the considered equations. In my opinion, these integral estimates, formulated in Propositons 2--7, may be useful for other authors studying mixed stochastic equations. The paper finishes with references which are representative for the studied problems.