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Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions with Hurst parameters H ∈ (1/3, 1/2]

 

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Opened Access Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions 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: 2015-10
Published in: Discrete and Continuous Dynamical Systems - Series B, 20 (8), 2553-2581.
Document type: Article
Abstract: In this article we are concerned with the study of the existence and uniqueness of pathwise mild solutions to evolutions equations driven by a H¨older continuous function with H¨older exponent in (1/3, 1/2). Our stochastic integral is a generalization of the well-known Young integral. To be more precise, the integral is defined by using a fractional integration by parts formula and it involves a tensor for which we need to formulate a new equation. From this it turns out that we have to solve a system consisting in a path and an area equations. In this paper we prove the existence of a unique local solution of the system of equations. The results can be applied to stochastic evolution equations with a non-linear diffusion coefficient driven by a fractional Brownian motion with Hurst parameter in (1/3, 1/2], which is particular includes white noise.
Cite: Garrido Atienza, M.J., Lu, K. y Schmalfuss, B. (2015). Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions with Hurst parameters H ∈ (1/3, 1/2]. Discrete and Continuous Dynamical Systems - Series B, 20 (8), 2553-2581.
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URI: http://hdl.handle.net/11441/44899

DOI: 10.3934/dcdsb.2015.20.2553

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