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Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters H∈(1/3,1/2]

 

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Opened Access Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters H∈(1/3,1/2]
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Author: Garrido Atienza, María José
Lu, Kening
Schmalfuss, Björn
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016
Published in: SIAM Journal on Applied Dynamical Systems, 15 (1), 625-654.
Document type: Article
Abstract: We consider the stochastic evolution equation du = Audt + G(u)dω, u(0) = u0 in a separable Hilbert space V . Here G is supposed to be three times Fr´echet-differentiable and ω is a trace class fractional Brownian motion with Hurst parameter H ∈ (1/3, 1/2]. We prove the existence of a unique pathwise global solution, and, since the considered stochastic integral does not produce exceptional sets, we are able to show that the above equation generates a random dynamical system.
Cite: Garrido Atienza, M.J., Lu, K. y Schmalfuss, B. (2016). Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters H∈(1/3,1/2]. SIAM Journal on Applied Dynamical Systems, 15 (1), 625-654.
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URI: http://hdl.handle.net/11441/43246

DOI: 10.1137/15M1030303

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