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Mat. Zametki, 2001, Volume 69, Issue 2, Pages 262–276 (Mi mz501)  

This article is cited in 5 scientific papers (total in 5 papers)

On Applications of Maslov Optimization Theory

P. Del Moral, M. Doisy

Université Paul Sabatier

Abstract: Maslov optimization theory has recently emerged as a new branch of functional analysis for studying deterministic control problems and Hamilton Jacobi equations. The main purpose of this work is to use an idempotent probability calculus to study the fixed points of nonexpansive transformations on nonnecessarily finite state spaces. We will see that these fixed points can be regarded as the $(\max,+)$-version of the invariant measure of Markov semi-groups. In the second part of this work we also present the $(\max,+)$-version of Dynkin's formula in the theory of stochastic processes and we apply this formula to study the stability properties of Bellman–Maslov processes.

DOI: https://doi.org/10.4213/mzm501

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English version:
Mathematical Notes, 2001, 69:2, 232–244

Bibliographic databases:

UDC: 517
Received: 10.04.1998

Citation: P. Del Moral, M. Doisy, “On Applications of Maslov Optimization Theory”, Mat. Zametki, 69:2 (2001), 262–276; Math. Notes, 69:2 (2001), 232–244

Citation in format AMSBIB
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\pages 232--244
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Truffet L., “Some ideas for comparison of Bellman chains”, Kybernetika (Prague), 39:2 (2003), 155–163  mathscinet  zmath  isi
    2. G. L. Litvinov, “The Maslov dequantization, idempotent and tropical mathematics: a brief introduction”, J. Math. Sci. (N. Y.), 140:3 (2007), 426–444  mathnet  crossref  mathscinet  zmath  elib  elib
    3. B. Kh. Kirshtein, G. L. Litvinov, “Analyzing stable regimes of electrical power systems and tropical geometry of power balance equations over complex multifields”, Autom. Remote Control, 75:10 (2014), 1802–1813  mathnet  crossref  isi
    4. Barbaresco F., “Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics”, Entropy, 16:8 (2014), 4521–4565  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Mazurenko N., Zarichnyi M., “Invariant Idempotent Measures”, Carpathian Math. Publ., 10:1 (2018), 172–178  crossref  zmath  isi
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