Wednesday, September 25, 2019 - 14:30 in X-E0-002
A Markov process for an infinite interacting particle system in the continuum
A talk in the Keine Reihe series by
Jurij Kozicki from Maria Curie-Sklodowska University, Lublin, Poland
| Abstract: |
An infinite system of point particles placed in a continuous habitat is studied.
Its constituents perform random jumps with mutual repulsion described by translation invariant jump kernel and interaction potential, respectively.
The pure states of this system are locally finite subsets of the habitat, which can also be interpreted as locally finite Radon measures.
For a special class of (sub-Poissonian) probability measures on the state space, there is proved that a restricted initial-value martingale problem employing sub-Poissonian measures has a unique solution.
Thereby, a Markov process with cadlag paths is constructed that describes the stochastic evolution of the considered particle system.
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