A white noise approach to stochastic partial differential equations driven by the fractional L??vy noise

摘要

In this paper, based on the white noise theory for d-parameter L??vy random fields given by (Holden et al. in Stochastic Partial Differential Equations: A modeling, white noise functional approach, 2010), we develop a white noise frame for anisotropic fractional L??vy random fields to solve the stochastic Poisson equation and the stochastic Schr??dinger equation driven by the d-parameter fractional L??vy noise. The solutions for the two kinds of equations are all strong solutions given explicitly in the L??vya??Hida stochastic distribution space.