Contemporary research supports the viewpoint that self-referential cognition is the proper
definition of life. From that initiating platform, a cohesive alternative evolutionary narrative …

In this paper we study the Wong–Zakai approximations given by a stationary process via the
Wiener shift and their associated long term pathwise behavior for the stochastic partial …

This paper is concerned with the invariant measures of non-autonomous stochastic reaction-
diffusion equations on unbounded domains. We firstly investigate the existence of invariant …

This paper addresses the exponential stability of the trivial solution of some types of
evolution equations driven by Hölder continuous functions with Hölder index greater than …

This paper is devoted to the existence of random attractors for rough partial differential
equations driven by nonlinear multiplicative Hölder rough paths with exponents in (1/3, 1/2] …

In this paper, we study the Wong–Zakai approximations given by a stationary process via the
Wiener shift and their associated dynamics of a class of stochastic evolution equations with …

The aim of this paper is to prove the existence and qualitative property of random attractors
for a stochastic non-local delayed reaction–diffusion equation (SNDRDE) on a semi-infinite …

In this paper, we first present some conditions for bounding the fractal dimension of a
random invariant set of a non-autonomous random dynamical system on a separable …

arXiv:1811.09517v2 [math.PR] 5 Apr 2019 Page 1 arXiv:1811.09517v2 [math.PR] 5 Apr 2019
Global solutions and random dynamical systems for rough evolution equations Robert Hesse∗ …

In this manuscript, we establish local exponential stability of the trivial solution of differential
equations driven by Hölder continuous paths with Hölder exponent greater than 1/2. This …