Reflected stochastic differential equations driven by standard and fractional Brownian motion

Abstract

The reflection problem on the positive half-line with reflection at zero for a time-dependent stochastic differential equations driven by standard and fractional Brownian motion with Hurst parameter [Formula: see text] is considered. We prove the existence of weak solutions by using Euler scheme. Moreover, we show that pathwise uniqueness holds and a strong solution exists in the case of additive fractional noise and also up to a stopping time [Formula: see text] for the multiplicative case, but remains an open question beyond [Formula: see text].