Abstract:We prove existence and uniqueness of the solution for 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 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… Show more
“…Existence and uniqueness of solutions to SDEs with discontinuous drift is true under very general conditions and has been studied in various setups, see, e.g., [43,36,37,38,14,42,20,34,15,39,16,40,32,21,33,35].…”
Section: Sdes With Irregular Coefficientsmentioning
Numerical methods for stochastic differential equations with non-globally Lipschitz coefficients are currently studied intensively. This article gives an overview of our work for the case that the drift coefficient is potentially discontinuous complemented by other important results in this area. To make the topic accessible to a broad audience, we begin with a heuristic on SDEs and a motivation.
“…Existence and uniqueness of solutions to SDEs with discontinuous drift is true under very general conditions and has been studied in various setups, see, e.g., [43,36,37,38,14,42,20,34,15,39,16,40,32,21,33,35].…”
Section: Sdes With Irregular Coefficientsmentioning
Numerical methods for stochastic differential equations with non-globally Lipschitz coefficients are currently studied intensively. This article gives an overview of our work for the case that the drift coefficient is potentially discontinuous complemented by other important results in this area. To make the topic accessible to a broad audience, we begin with a heuristic on SDEs and a motivation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.