Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
Probability
2022-01-27 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0801.4963,
title = {Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion},
author = {João Guerra and David Nualart},
journal= {arXiv preprint arXiv:0801.4963},
year = {2022}
}
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21 pages