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Feynman-Kac formula for Levy processesand semiclassical (Euclidean) momentum representation
Nanyang Technological University. (School of Physical and Mathematical Sciences)
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Universidade de Lisboa. (Grupo de Fisica Matematica)
2014 (English)In: Markov Processes and Related Fields, ISSN 1024-2953, Vol. 20, no 3, 577-600 p.Article in journal (Refereed) Published
Abstract [en]

We prove a version of the Feynman-Kac formula for Levy processes andintegro-differential operators, with application to the momentum representationof suitable quantum (Euclidean) systems whose Hamiltonians involve L´evytypepotentials. Large deviation techniques are used to obtain the limitingbehavior of the systems as the Planck constant approaches zero. It turns outthat the limiting behavior coincides with fresh aspects of the semiclassical limitof (Euclidean) quantum mechanics. Non-trivial examples of Levy processes areconsidered as illustrations and precise asymptotics are given for the terms inboth configuration and momentum representations.

Place, publisher, year, edition, pages
2014. Vol. 20, no 3, 577-600 p.
Keyword [en]
Levy process, Feynman-Kac type formula, momentum representation, large deviations
National Category
Probability Theory and Statistics
URN: urn:nbn:se:liu:diva-112752ISI: 000345889000012OAI: diva2:771410
Available from: 2014-12-13 Created: 2014-12-13 Last updated: 2015-01-19Bibliographically approved

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Yang, Xiangfeng
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Mathematical Statistics The Institute of Technology
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