Uniqueness for a historical SDE with a singular interaction
It is proved the existence and pathwise uniqueness for a stochastic differential equation where the drift part has a discontinuity and evolves in a nonlinear manner. Approximating the singular drift by a bounded and globally Lipschitz continuous function and using Perkins theorem are the main tools for proving the issues. The paper is written in a clear manner, and proofs are given in detail. It is recommended for mathematicians specialized in stochastic differential equations.
scientific article; zbMATH DE number 1208797