Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm

Abstract

This paper studies the periodic stochastic high-order Degasperis–Procesi (DP) equation driven by a cylindrical fractional Brownian motion (fBm) which is white in space. And it has the covariance with Hurst parameter [Formula: see text] in the time variable. The local existence and uniqueness of the solution [Formula: see text] in [Formula: see text] with [Formula: see text] are proved by fixed point theorem combined with the stochastic term estimations in the Besov-type Bourgain space [Formula: see text] and the second iteration of non-linear term.