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1 results

  • On mixed fractional stochastic differential equations with discontinuous drift coefficient

  • Part of
  • Ercan Sönmez
  • Journal:
    Journal of Applied Probability / Volume 60 / Issue 2 / June 2023
    Published online by Cambridge University Press:
    01 December 2022, pp. 589-606
    Print publication:
    June 2023
    • Article
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  • We prove existence and uniqueness for the solution of a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with an absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient.