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ЖУРНАЛЫ // Theory of Stochastic Processes // Архив

Theory Stoch. Process., 2020, том 25(41), выпуск 2, страницы 74–80 (Mi thsp319)

On number of particles in coalescing-fragmentating Wasserstein dynamics

Vitalii V. Konarovskyiabc

a Faculty of Mathematics, Computer Science and Natural Sciences, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
b Institute of Mathematics, University of Leipzig, Augustusplatz 10, 04109 Leipzig, Germany
c Institute of Mathematics of NAS of Ukraine, Tereschenkivska st. 3, 01024 Kiev, Ukraine

Аннотация: We consider the system of sticky-reflected Brownian particles on the real line proposed in [4]. The model is a modification of the Howitt-Warren flow but now the diffusion rate of particles is inversely proportional to the mass which they transfer. It is known that the system consists of a finite number of distinct particles for almost all times. In this paper, we show that the system also admits an infinite number of distinct particles on a dense subset of the time interval if and only if the function responsible for the splitting of particles takes an infinite number of values.

Ключевые слова: Sticky-reflected particle system, modified massive Arratia flow, infinite dimensional singular SDE.

MSC: Primary 60K35, 60H05; Secondary 60H05, 60G44

Язык публикации: английский



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