A Study of Parabolic and Hyperbolic Anderson Models Driven by Fractional Brownian Sheet with Spatial Hurst Index in (0,1)
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...
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| Format: | Others |
| Language: | en |
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Université d'Ottawa / University of Ottawa
2020
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| Online Access: | http://hdl.handle.net/10393/40721 http://dx.doi.org/10.20381/ruor-24949 |
| Summary: | 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. |
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