A Study of Parabolic and Hyperbolic Anderson Models Driven by Fractional Brownian Sheet with Spatial Hurst Index in (0,1)

• Main Author: Ma, Yiping
• Other Authors: Balan, Raluca Madalina
• Format: Others
• Language: en
• Published: Université d'Ottawa / University of Ottawa 2020
• Subjects: Parabolic and Hyperbolic Anderson models; fractional Brownian sheet
• Online Access: http://hdl.handle.net/10393/40721; http://dx.doi.org/10.20381/ruor-24949

The goal of this thesis is to present a comprehensive study of the parabolic and hyperbolic Anderson models with constant initial condition, driven by a Gaussian noise which is fractional in space with index H > 1/2 or H < 1/2, and is either white in time, or fractional in time with index H_0 > 1/2. As a preliminary step, we study the linear stochastic heat and wave equations with the same type of noise. In the case H_0 > 1/2 and H < 1/2, we present a new result, regarding the solution of the parabolic Anderson model with general initial condition given by a measure.