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Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

Jo\~ao Guerra and David Nualart
Arxiv ID: 0801.4963Last updated: 1/27/2022
We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the classical Ito stochastic calculus. The existence result is based on the Yamada-Watanabe theorem.

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