Probabilistic approach for semi-linear stochastic fractal equations

Yingchao Xie, Qi Zhang and Xicheng Zhang

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 3948-3964

Abstract: In this work we provide a stochastic representation for a class of semi-linear stochastic fractal equations, and prove the existence and uniqueness of Wρ1,p-solutions to stochastic fractal equations by using purely probabilistic argument, where ρ is a suitable weighted function, and Wρ1,p is the associated first order weighted Sobolev space.

Keywords: α-stable processes; Stochastic fractal equations; Stochastic flows; Derivative formula (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:12:p:3948-3964

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DOI: 10.1016/j.spa.2014.07.007

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