Stationary points in coalescing stochastic flows on R

Andrey A. Dorogovtsev, Georgii V. Riabov and Björn Schmalfuß

Stochastic Processes and their Applications, 2020, vol. 130, issue 8, 4910-4926

Abstract: 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 dX(t)=a(X(t))dt+dw(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.

Keywords: Stochastic flow; Coalescence; Random dynamical system; Invariant measure (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:8:p:4910-4926

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DOI: 10.1016/j.spa.2020.02.005

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