Weak convergence of path-dependent SDEs 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 $H\in (1/2,1)$.

arXiv comment26 pages

References in corpus (8)

• The rate of convergence of Euler approximations for solutions of stochastic differential equations driven by fractional Brownian motion
• Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions
• Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions
• Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion
• Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index $H>1/2$
• Approximation of fractional Brownian motion by martingales
• Weak convergence of path-dependent SDEs with irregular coefficients
• Moment estimates and applications for SDEs driven by fractional Brownian motion with irregular drifts

Cited by in corpus (1)

• On mixed fractional SDEs with discontinuous drift coefficient