Doubly Perturbed Distribution Dependent Stochastic Differential Equation

Abstract

In this article, we discuss a class of doubly perturbed distribution dependent stochastic differential equations (SDEs). We give some sufficient conditions to ensure the existence and uniqueness of solutions to the considered equations under some weak conditions, where a convex combination of the Nagumo and Osgood conditions is taken into consideration. Meanwhile, our results extend the classical hypothesis ∣α∣ + ∣β∣ < 1 on the perturbed intensity α and β to the generalized case. And then, we study the stability properties in regard to the initial value and coefficients.

Keywords

Doubly perturbed SDEs / existence and uniqueness / Nagumo and Osgood conditions / 60H15 / 60G15 / 60H05

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