On mixed fractional stochastic differential equations with discontinuous drift coefficient

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 der...

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Bibliographic Details
Published in:Journal of applied probability 2023-06, Vol.60 (2), p.589-606
Main Author: Sönmez, Ercan
Format: Article
Language:English
Subjects:
Brownian motion
Convex analysis
Differential equations
Diffusion coefficient
Drift
Mathematical analysis
Original Article
Uniqueness
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Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2022.71