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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 2, Pages 384–400
DOI: https://doi.org/10.4213/tvp774 (Mi tvp774) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Maslov idempotent probability calculus. II

P. Del Morala, M. Doisyab

a LSP-UMR, CNRS, Univ. Paul Sabatier, France
b ENSEEIHT, France
Full-text PDF (815 kB) Citations (15)
DOI: https://doi.org/10.4213/tvp774
Abstract: The study of Bellman–Maslov processes has lead to new advances in the understanding of optimal control problems and of its relation to the study of Hamilton–Jacobi differential equations. The aim of this work is to show that idempotent calculus yields a natural and general probabilistic line of thought for studying such equations. Some new results relating to the long-time behavior of the solution of a class of Hamilton–Jacobi differential equations can be regarded as a $(\max,+)$-version of the law of large numbers and the central limit theorem. The applications to some evolution equation arising in mathematical morphology are also discussed.
Keywords: Bellman–Maslov processes, Hamilton–Jacobi equations, idempotent calculus, mathematical morphology.
Received: 10.06.1998
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 2, Pages 319–332
DOI: https://doi.org/10.1137/S0040585X97977598
Bibliographic databases:
Language: English
Citation: P. Del Moral, M. Doisy, “Maslov idempotent probability calculus. II”, Teor. Veroyatnost. i Primenen., 44:2 (1999), 384–400; Theory Probab. Appl., 44:2 (2000), 319–332
Citation in format AMSBIB
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\paper Maslov idempotent probability calculus.~II
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\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 2
\pages 319--332
\crossref{https://doi.org/10.1137/S0040585X97977598}
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  • https://doi.org/10.4213/tvp774
  • https://www.mathnet.ru/eng/tvp/v44/i2/p384
    Cycle of papers
    This publication is cited in the following 15 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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