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Note on Negative Probabilities and Observable Processes

Authors: Ulrich Faigle and Alexander Schoenhuth

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract

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.

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Ulrich Faigle and Alexander Schoenhuth. Note on Negative Probabilities and Observable Processes. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{faigle_et_al:DagSemProc.05031.19,
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.19},
  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}
}

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Note on Negative Probabilities and Observable Processes

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