2018/08/17 by Dorogovtsev, Andrey A., Riabov, Georgii V., Schmalfuß, Björn
#37H15 #60G51 #60H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1808.05969
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 (constructed in \citeRiabov) 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.