On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order
Seyfeddine Moualkia, Yong Xu
Abstract
Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of their solutions in this case. This paper is about the existence and uniqueness of solutions to the fractional stochastic differential equations with variable order. We prove the existence by using the Picard iterations and propose new sufficient conditions for the uniqueness.
Topics & Concepts
UniquenessMathematicsVariable (mathematics)Order (exchange)Differential equationStochastic differential equationApplied mathematicsMathematical analysisStochastic partial differential equationFinanceEconomicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStochastic processes and financial applications