Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise
type: Item
instance of: scholarly article
title: Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise
zbMATH Open document ID: 1328.60143
DOI: 10.1155/2014/601327
author: Caibin Zeng
author: Junfei Cao
author: Qi-Gui Yang
published in: The Scientific World Journal. Probability and Statistics
publication date: 2016-01-13T00:00:00Z
review text: Summary: This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient \(\Phi:dX(t)=A(X(t))dt+\Phi(t)dB^H(t)\), where \(A\) is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized \(p\)-Laplacian equation.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 6529680
Wikidata QID: Q51107807
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/601327
OpenAlex ID: W1983827087
cites work: Arbitrage with Fractional Brownian Motion
cites work: Stochastic analysis of the fractional Brownian motion
cites work: Stochastic analysis of fractional brownian motions
cites work: Itô's formula with respect to fractional Brownian motion and its application
cites work: Stochastic Calculus for Fractional Brownian Motion I. Theory
cites work: Stochastic calculus with respect to Gaussian processes
cites work: Stochastic integration with respect to fractional Brownian motion
cites work: A General Fractional White Noise Theory And Applications To Finance
cites work: An introduction to white–noise theory and Malliavin calculus for fractional Brownian motion
cites work: Differential equations driven by fractional Brownian motion
cites work: Q4210478
cites work: Random Dynamical Systems and Stationary Solutions of Differential Equations Driven by the Fractional Brownian Motion
cites work: Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion
cites work: RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION
cites work: Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion
cites work: The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion
cites work: A concise course on stochastic partial differential equations
cites work: Random attractors for a class of stochastic partial differential equations driven by general additive noise
cites work: Q3995203
cites work: FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
cites work: A NOTE ON VARIATIONAL SOLUTIONS TO SPDE PERTURBED BY GAUSSIAN NOISE IN A GENERAL CLASS
cites work: SPDE in Hilbert space with locally monotone coefficients
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description: scientific article; zbMATH DE number 6529680