Analytic and Probabilistic Aspects of Lévy Processes and Fields in Quantum Theory

Sergio Albeverio (), Barbara Rüdiger () and Jiang-Lun Wu ()
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Sergio Albeverio: Universität Bonn, Institut für Angewandte Mathematik, SFB 256
Barbara Rüdiger: Universität Bonn, Institut für Angewandte Mathematik, SFB 256
Jiang-Lun Wu: Universität Bonn, Institut für Angewandte Mathematik, SFB 256

A chapter in Lévy Processes, 2001, pp 187-224 from Springer

Abstract: Abstract A review of work on the description of generators and processes associated with stochastic (partial or pseudo-) differential equations driven by general white noises (including jump as well as diffusion parts) is given. Processes with finite- or infinite-dimensional state space are described in a unified way using the theory of Dirichlet forms, combined with the technique of subordination of processes. In particular the analytic problems arising from subordinating sub-Markov semigroups are described. As examples the subordination of stochastic quantization processes is presented. It is also described how stochastic partial differential or pseudodifferential equations are used to construct relativistic quantum fields in indefinite metric with nontrivial scattering in four space- time dimensions.

Keywords: Stochastic Differential Equation; Pseudodifferential Operator; Dirichlet Form; Stochastic Partial Differential Equation; Martingale Problem (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0197-7_9

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DOI: 10.1007/978-1-4612-0197-7_9

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