Poisson Series Approaches to Bayesian Monte Carlo Inference for Skewed alpha-Stable Distributions and Stochastic Processes

Beschreibung

This thesis addresses inference for alpha-stable distributions and Lévy processes. Based on approximated series representations of the stable laws and the corresponding stable stochastic integrals, conditionally Gaussian distributions are provided. Therefore, inference can be carried out straightforwardly using Bayesian computational methods such as Markov chain Monte Carlo methods and Rao-Blackwellised particle filters. Discrete- and continuous-time autoregressive models driven by stable processes, as well as alpha-stable distributions serve to illustrate the parameter and state estimation

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Tatjana Lemke

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