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A white noise approach to stochastic partial differential equations driven by the fractional Lévy noise. (English) Zbl 1448.60142
Summary: In this paper, based on the white noise theory for $$d$$-parameter Lévy random fields given by H. Holden et al. [Stochastic partial differential equations. A modeling, white noise functional approach. 2nd ed. New York, NY: Springer (2010; Zbl 1198.60005)], 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.
##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60H40 White noise theory 60G51 Processes with independent increments; Lévy processes 60G52 Stable stochastic processes
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