Second order elliptic partial differential equations driven by L\'evy white noise
Abstract
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'evy white noise. We first derive an existence theorem for integral transforms of L\'evy white noise and prove the existence of generalized and mild solutions of second order elliptic partial differential equations. Furthermore, we discuss the generalized electric Schr\"odinger operator for different potential functions V.
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