Weak convergence of SFDEs driven by fractional Brownian motion with irregular coefficients

Abstract

In this paper, by using Girsanov’s transformation and the property of the corresponding reference stochastic differential equations, we investigate weak existence and uniqueness of solutions and weak convergence of Euler-Maruyama scheme to stochastic functional differential equations with Hölder continuous drift driven by fractional Brownian motion with Hurst index $H\in (1/2,1).$

Keywords:

• Weak solution
• weak convergence
• Hölder continuity drift
• fractional Brownian motion

AMS Subject Classification:

• 60F10
• 60H10
• 34K26

Additional information

Funding

The authors would like to thank referees’ useful comments and suggestions. This work was supported by the disciplinary funding of Central University of Finance and Economics; [National Natural Science Foundation of China] under Grant [number 11901604].