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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 4, Pages 735–751
DOI: https://doi.org/10.4213/tvp2029 (Mi tvp2029) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Maslov idempotent probability calculus, I

P. Del Morala, M. Doisyab

a LSP-UMR, Univ. Paul Sabatier, France
b ENSEEIHT, France
Full-text PDF (2408 kB) Citations (24)
DOI: https://doi.org/10.4213/tvp2029
Abstract: Maslov's idempotent measures allow an optimization theory to be derived at the same level of generality as probability and stochastic process theory. One purpose of this work is to present the basic concepts of this $(\max,+)$-version of probability theory. Using this framework we will see that the Bellman optimality principle is the idempotent version of the classical Markov causality principle. Applications to optimal control problems, Hamilton–Jacobi equations, and mathematical morphology are discussed in the second part of this study.
Keywords: optimization theory, Maslov idempotent measure, idempotent probability calculus, Bellman–Markov processes.
Received: 10.06.1998
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 4, Pages 562–576
DOI: https://doi.org/10.1137/S0040585X97977161
Bibliographic databases:
Language: English
Citation: P. Del Moral, M. Doisy, “Maslov idempotent probability calculus, I”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 735–751; Theory Probab. Appl., 43:4 (1999), 562–576
Citation in format AMSBIB
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\by P.~Del Moral, M.~Doisy
\paper Maslov idempotent probability calculus,~I
\jour Teor. Veroyatnost. i Primenen.
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\pages 735--751
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\zmath{https://zbmath.org/?q=an:0952.60001}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 4
\pages 562--576
\crossref{https://doi.org/10.1137/S0040585X97977161}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000085137600003}
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  • https://www.mathnet.ru/eng/tvp/v43/i4/p735
    Cycle of papers
    This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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