Impulsive stochastic fractional differential equations driven by fractional Brownian motion
Mahmoud Abouagwa, Feifei Cheng, Ji Li
Abstract
Abstract In this research, we study the existence and uniqueness results for a new class of stochastic fractional differential equations with impulses driven by a standard Brownian motion and an independent fractional Brownian motion with Hurst index $1/2< H<1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo><</mml:mo><mml:mi>H</mml:mi><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math> under a non-Lipschitz condition with the Lipschitz one as a particular case. Our analysis depends on an approximation scheme of Carathéodory type. Some previous results are improved and extended.
Topics & Concepts
Fractional Brownian motionHurst exponentBrownian motionUniquenessMathematicsLipschitz continuityOrdinary differential equationMathematical analysisDifferential equationStatisticsNonlinear Differential Equations AnalysisStochastic processes and financial applicationsFractional Differential Equations Solutions