Orbital Stability of Patterns in Semilinear SPDE using a Multiscale Analysis

In this thesis we consider orbital stability of certain patterns in stochastic partial differential equations. We study two examples: a rotating wave in a two-dimensional reaction-diffusion equation and a soliton in a parametrically forced nonlinear Schrödinger equation. In both cases, we show that, for small noise, solutions to the stochastic...

Spatiotemporal Gaussian random fields using stochastic partial differential equations

In various scientific disciplines, measurement data is collected across space and over time with the aim of inferring information regarding an underlying stochastic spatiotemporal phenomenon. The high computational costs of current methods render this task intractable for the large datasets typically encountered in spatiotemporal statistics. <br...

Fourier Spectral Methods for Bayesian Filtering of Stochastic Partial Differential Equations

The development of computationally ecient algorithms for statistical inference of stochastic dierential equations has been a long-standing research subject ever since the advent of stochastic analysis. Recently, there has been an increasing interest in extending these methods to the statistical study of stochastic partial dierential equations....