Publication: Correlated coalescing Brownian flows on R and the circle
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Hajri, Hatem
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NO
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Abstract
We consider a stochastic differential equation on the real line which is driven by two correlated Brownian motions B+ and B- respectively on the positive half line and the negative half line. We assume vertical bar d < B+, B->(t)vertical bar <= rho dt with rho is an element of [0, 1). We prove it has a unique flow solution. Then, we generalize this flow to a flow on the circle, which represents an oriented graph with two edges and two vertices. We prove that both flows are coalescing. Coalescence leads to the study of a correlated reflected Brownian motion on the quadrant. Moreover, we find the distribution of the hitting time to the origin of a reflected Brownian motion. This has implications for the effect of the correlation coefficient rho on the coalescence time of our flows.
Source
Publisher
The International Marine Purchasing Association (IMPA)
Subject
Statistics and probability
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Has Part
Source
Alea- Latin American Journal of Probability and Mathematical Statistics
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Edition
DOI
10.30757/ALEA.v15-54