Sweeping processes with stochastic perturbations generated by a fractional Brownian motion

Abstract

We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation results for deterministic sweeping processes with bounded $p$-variation and next we apply them to the stochastic case.

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• One-dimensional reflected rough differential equations