A white noise approach to stochastic partial differential equations driven by the fractional Lévy noise

Abstract

Abstract In this paper, based on the white noise theory for d-parameter Lévy 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 Lévy random fields to solve the stochastic Poisson equation and the stochastic Schrödinger equation driven by the d-parameter fractional Lévy noise. The solutions for the two kinds of equations are all strong solutions given explicitly in the Lévy–Hida stochastic distribution space.

Keywords

• White noise analysis
• Anisotropic fractional Lévy noises
• Stochastic Poisson equation
• Stochastic Schrödinger equation