| Superpositions of probability distributions. | |
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MedLine Citation:
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PMID: 18851008 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances v=sigma;{2} play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian processes because they may introduce memory effects. We derive the general form of the smearing distributions in v which do not destroy the semigroup property. The smearing technique has two immediate applications. It permits simplifying the system of Kramers-Moyal equations for smeared and unsmeared conditional probabilities, and can be conveniently implemented in the path integral calculus. In many cases, the superposition of path integrals can be evaluated much easier than the initial path integral. Three simple examples are presented, and it is shown how the technique is extended to quantum mechanics. |
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Authors:
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Petr Jizba; Hagen Kleinert |
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Publication Detail:
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Type: Journal Article Date: 2008-09-17 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 78 ISSN: 1539-3755 ISO Abbreviation: Phys Rev E Stat Nonlin Soft Matter Phys Publication Date: 2008 Sep |
Date Detail:
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Created Date: 2008-10-14 Completed Date: 2008-12-04 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: United States |
Other Details:
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Languages: eng Pagination: 031122 Citation Subset: - |
Affiliation:
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ITP, Freie Universität Berlin, Arnimallee 14 D-14195 Berlin, Germany. jizba@physik.fu-berlin.de |
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