20 research outputs found
Stochastic lattice dynamical systems with fractional noise
This article is devoted to study stochastic lattice dynamical systems driven
by a fractional Brownian motion with Hurst parameter . First of
all, we investigate the existence and uniqueness of pathwise mild solutions to
such systems by the Young integration setting and prove that the solution
generates a random dynamical system. Further, we analyze the exponential
stability of the trivial solution
Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in
This paper addresses the exponential stability of the trivial solution of
some types of evolution equations driven by H\"older continuous functions with
H\"older index greater than . The results can be applied to the case of
equations whose noisy inputs are given by a fractional Brownian motion
with covariance operator , provided that and is
sufficiently small.Comment: 19 page
Synchronization in infinite-dimensional deterministic and stochastic systems
The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics