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

Abstract

In this paper, 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 ∈ (1/2, 1). The methods used in this paper are Girsanov's transformation and the property of the corresponding reference stochastic differential equations.

On mixed fractional stochastic differential equations with discontinuous drift coefficient

“…Comparatively little is known for purely fractional SDEs, i.e. , with discontinuous drift coefficient; see [1, 13, 25] for the case . In [13, Theorem 3.5.14] the existence of a strong solution is proven for purely fractional SDEs with additive noise, where the drift coefficient is given by the discontinuous function for all and the Hurst index H is restricted to ; see also [14, Theorem 1] for a related result.…”