Probabilistic approach for semi-linear stochastic fractal equations

摘要

In this work we provide a stochastic representation for a class of semi-linear stochastic fractal equations, and prove the existence and uniqueness of W_ρ~(1,p) -solutions to stochastic fractal equations by using purely probabilistic argument, where ρ is a suitable weighted function, and W_ρ~(1,p) is the associated first order weighted Sobolev space.