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

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

2008-01-31

arxiv.org/abs/0801.4963v1

Mathematics

Probability

21 pages

Scientific paper

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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