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Markov evolutions and hierarchical equations in the continuum. I: one-component systems

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Abstract

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.

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Authors and Affiliations

  1. Institute of Mathematics of UNAS, 3, Tereshchenkivska str., 01601, Kiev-4, Ukraine

    Dmitri L. Finkelshtein

  2. Fakultät für Mathematik, Universität Bielefeld, Postfach 100 131, 33501, Bielefeld, Germany

    Yuri G. Kondratiev

  3. Universidade Aberta, 1269-001, Lisbon, Portugal

    Maria Joã o Oliveira

  4. Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisbon, Portugal

    Maria Joã o Oliveira

  5. Forschungszentrum BiBoS, Universität Bielefeld, 33615, Bielefeld, Germany

    Yuri G. Kondratiev & Maria Joã o Oliveira

Authors
  1. Dmitri L. Finkelshtein
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  2. Yuri G. Kondratiev
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  3. Maria Joã o Oliveira
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Correspondence to Maria Joã o Oliveira.

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Finkelshtein, D.L., Kondratiev, Y.G. & Oliveira, M.J. Markov evolutions and hierarchical equations in the continuum. I: one-component systems. J. Evol. Equ. 9, 197–233 (2009). https://doi.org/10.1007/s00028-009-0007-9

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  • DOI: https://doi.org/10.1007/s00028-009-0007-9

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