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978-3-8439-1454-3, Reihe Mathematik

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

135 Seiten, Dissertation Technische Universität Kaiserslautern (2014), Softcover, B5

Zusammenfassung / Abstract

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