Department of Mathematics2024-11-0920181980-043610.30757/ALEA.V15-542-s2.0-85070019641http://dx.doi.org/10.30757/ALEA.V15-54https://hdl.handle.net/20.500.14288/10400We 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 |d〈B+,B-〉t| ≤ ρ dt with ρ ∈ [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 ρ on the coalescence time of our flows.StatisticsProbabilityJournal Articlehttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85070019641&doi=10.30757%2fALEA.V15-54&partnerID=40&md5=cc447dd74bb381e321bfae5fae3e8ba34604758000271232