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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.
  • 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. (en)
Title
  • Superpositions of Probability Distributions
  • Superpositions of Probability Distributions (en)
skos:prefLabel
  • Superpositions of Probability Distributions
  • Superpositions of Probability Distributions (en)
skos:notation
  • RIV/68407700:21340/08:00153949!RIV10-MSM-21340___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM6840770039)
http://linked.open...iv/cisloPeriodika
  • 3
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
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  • 398370
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  • RIV/68407700:21340/08:00153949
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • probability distributions; semigroups (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [88F5835F6914]
http://linked.open...i/riv/nazevZdroje
  • Physical Review E
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 78
http://linked.open...iv/tvurceVysledku
  • Jizba, Petr
http://linked.open...ain/vavai/riv/wos
  • 000259682700029
http://linked.open...n/vavai/riv/zamer
issn
  • 1539-3755
number of pages
http://localhost/t...ganizacniJednotka
  • 21340
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