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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