Pullback attractors for stochastic Young differential delay equations

TL;DR

This paper investigates the long-term behavior of stochastic Young differential delay equations, demonstrating the existence of a random pullback attractor under certain spectral and Lipschitz conditions.

Contribution

It establishes conditions for the existence of a random pullback attractor in stochastic delay equations with a linear drift component and small Lipschitz coefficients.

Findings

Existence of a random pullback attractor under specified conditions.

Linear drift with negative eigenvalues ensures stability.

Small Lipschitz coefficients are crucial for attractor existence.

Abstract

We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term which has no delay factor and has eigenvalues of negative real parts, then the generated random dynamical system possesses a random pullback attractor provided that the Lipschitz coefficients of the remaining parts are small.