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

In: Lévy Processes

Author

Listed:
  • Sergio Albeverio

    (Universität Bonn, Institut für Angewandte Mathematik, SFB 256
    SFB 237
    BiBoS-Research Centre
    CERFIM)

  • Barbara Rüdiger

    (Universität Bonn, Institut für Angewandte Mathematik, SFB 256)

  • Jiang-Lun Wu

    (Universität Bonn, Institut für Angewandte Mathematik, SFB 256
    University of Wales Swansea, Department of Mathematics
    Academia Sinica, Institute of Applied Mathematics)

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.

Suggested Citation

  • Sergio Albeverio & Barbara Rüdiger & Jiang-Lun Wu, 2001. "Analytic and Probabilistic Aspects of Lévy Processes and Fields in Quantum Theory," Springer Books, in: Ole E. Barndorff-Nielsen & Sidney I. Resnick & Thomas Mikosch (ed.), Lévy Processes, pages 187-224, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0197-7_9
    DOI: 10.1007/978-1-4612-0197-7_9
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