Random jumps and coalescence in the continuum: evolution of states of an infinite system

2018/07/19 by Yuri Kozitsky, Kozitsky, Yuri, Krzysztof Pilorz +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60K35 #82C22 #Dynamical Systems (math.DS) #FOS: Mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1807.07310

openalex publication_date 2018/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The dynamics of an infinite continuum system of randomly jumping and coalescing point particles is studied. The states of the system are probability measures on the corresponding configuration space Γ the evolution of which is constructed in the following way. The evolution of observables F₀→ F_t is obtained from a Kolmogorov-type evolution equation. Then the evolution of states μ₀→ μ_t is defined by the relation μ₀(F_t) =μ_t(F₀) for F₀ belonging to a measure-defining class of functions. The main result of the paper is the proof of the existence of the evolution of this type for a bounded time horizon.

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