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DOI: 10.4230/DagSemProc.05031.19
URN: urn:nbn:de:0030-drops-1087
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Faigle, Ulrich ; Schoenhuth, Alexander

Note on Negative Probabilities and Observable Processes

05031.FaigleUlrich.Paper.108.pdf (0.2 MB)


A mathematical framework for observable processes is introduced via the model of systems whose states may be time dependent and described by possibly "negative probabilities". The model generalizes and includes the linearly dependent models or observable operator models for classical discrete stochastic processes. Within this model a general convergence result for finite-dimensional processes, which generalize finite state (hidden) Markov models, is derived. On the philosophical side, the model furthermore offers an explanation for Bell's inequality in quantum mechanics.

BibTeX - Entry

  author =	{Faigle, Ulrich and Schoenhuth, Alexander},
  title =	{{Note on Negative Probabilities and Observable Processes}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-1087},
  doi =		{10.4230/DagSemProc.05031.19},
  annote =	{Keywords: Negative Probability , Observable Process , Markov Chain , Stochastic Process , Bell\~{A}¢\^{a}‚¬\^{a}„¢s Inequality , HHM , LDP , OOM}

Keywords: Negative Probability , Observable Process , Markov Chain , Stochastic Process , Bell’s Inequality , HHM , LDP , OOM
Collection: 05031 - Algorithms for Optimization with Incomplete Information
Issue Date: 2005
Date of publication: 09.06.2005

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