Stationary points in coalescing stochastic flows on R

Autor:	Andrey A. Dorogovtsev, Georgii V. Riabov, Björn Schmalfuß
Rok vydání:	2020
Předmět:	Statistics and Probability Work (thermodynamics) Stochastic differential equation Monotone polygon Pullback Flow (mathematics) Applied Mathematics Modeling and Simulation Mathematical analysis Random dynamical system Lipschitz continuity Stationary point Mathematics
Zdroj:	Stochastic Processes and their Applications. 130:4910-4926
ISSN:	0304-4149
DOI:	10.1016/j.spa.2020.02.005
Popis:	This work is devoted to long-time properties of the Arratia flow with drift – a stochastic flow on R whose one-point motions are weak solutions to a stochastic differential equation d X ( t ) = a ( X ( t ) ) d t + d w ( t ) that move independently before the meeting time and coalesce at the meeting time. We study special modification of such flow that gives rise to a random dynamical system and thus allows to discuss stationary points. Existence of a unique stationary point is proved in the case of a strictly monotone Lipschitz drift by developing a variant of a pullback procedure. Connections between the existence of a stationary point and properties of a dual flow are discussed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::33d07bc921d7fc9967bc26904dae48fe https://doi.org/10.1016/j.spa.2020.02.005 Zobrazit plný text záznamu Full Text from ScienceDirect