### A Markov process for an infinite interacting particle system in the continuum

Kozitsky Y, Röckner M (2021)
Electronic Journal of Probability 26: 1-53.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Kozitsky, Yuri; Röckner, MichaelUniBi
Einrichtung
Abstract / Bemerkung
An infinite system of point particles placed in R-d is studied. Its constituents perform random jumps (walks) with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states of the system are locally finite subsets of R-d, which can also be interpreted as locally finite Radon measures. The set of all such measures Gamma is equipped with the vague topology and the corresponding Borel sigma-field. For a special class P-exp of (sub-Poissonian) probability measures on Gamma, we prove the existence of a unique family {P-t,P-mu : t >= 0, mu is an element of P-exp} of probability measures on the space of cadlag paths with values in that solves a restricted initial-value martingale problem for the mentioned system. Thereby, a Markov process with cadlag paths is specified which describes the stochastic dynamics of this particle system.
Stichworte
Measure-valued Markov process; point process; martingale solution; Fokker-Planck equation; stochastic semigroup
Erscheinungsjahr
2021
Zeitschriftentitel
Electronic Journal of Probability
Band
26
Seite(n)
1-53
eISSN
1083-6489
Page URI
https://pub.uni-bielefeld.de/record/2955376

### Zitieren

Kozitsky Y, Röckner M. A Markov process for an infinite interacting particle system in the continuum. Electronic Journal of Probability . 2021;26:1-53.
Kozitsky, Y., & Röckner, M. (2021). A Markov process for an infinite interacting particle system in the continuum. Electronic Journal of Probability , 26, 1-53. https://doi.org/10.1214/21-EJP631
Kozitsky, Y., and Röckner, M. (2021). A Markov process for an infinite interacting particle system in the continuum. Electronic Journal of Probability 26, 1-53.
Kozitsky, Y., & Röckner, M., 2021. A Markov process for an infinite interacting particle system in the continuum. Electronic Journal of Probability , 26, p 1-53.
Y. Kozitsky and M. Röckner, “A Markov process for an infinite interacting particle system in the continuum”, Electronic Journal of Probability , vol. 26, 2021, pp. 1-53.
Kozitsky, Y., Röckner, M.: A Markov process for an infinite interacting particle system in the continuum. Electronic Journal of Probability . 26, 1-53 (2021).
Kozitsky, Yuri, and Röckner, Michael. “A Markov process for an infinite interacting particle system in the continuum”. Electronic Journal of Probability 26 (2021): 1-53.

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