3 research outputs found
Weak Pullback Mean Random Attractors for Stochastic Evolution Equations and Applications
In this paper, we investigate the existence and uniqueness of weak pullback
mean random attractors for abstract stochastic evolution equations with general
diffusion terms in Bochner spaces. As applications, the existence and
uniqueness of weak pullback mean random attractors for some stochastic models
such as stochastic reaction-diffusion equations, the stochastic -Laplace
equation and stochastic porous media equations are established.Comment: Few details were improved. Comments are welcom
Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters
We consider the stochastic evolution equation in a separable Hilbert--space . Here is supposed to be three
times Fr\'echet--differentiable and is a trace class fractional
Brownian--motion with Hurst parameter . We prove the existence
of a global solution where exceptional sets are independent of the initial
state . In addition, we show that the above equation generates a
random dynamical system.Comment: 29 page
Bilinear equations in Hilbert space driven by paths of low regularity
In the article, some bilinear evolution equations in Hilbert space driven by
paths of low regularity are considered and solved explicitly. The driving paths
are scalar-valued and continuous, and they are assumed to have a finite -th
variation along a given sequence of partitions in the sense given by Cont and
Perkowski \cite{ConPer18} ( being an even positive integer). Typical
functions that satisfy this condition are trajectories of the fractional
Brownian motion of the Hurst parameter H=\sfrac{1}{p}. A strong solution to
the bilinear problem is shown to exist if there is a solution to a certain
temporally inhomogeneous initial value problem. Subsequently, sufficient
conditions for the existence of the solution to this initial value problem are
given. The abstract results are applied to several stochastic partial
differential equations with multiplicative fractional noise, both of the
parabolic and hyperbolic type, that are solved explicitly in a pathwise sense.Comment: 27 Page