Kaynaşan iki Brown akışı: İlintili ve sıralı katsayılı

We consider a stochastic differential equation on the real line which is driven by two correlated Brownian motions respectively on the positive half line and the negative half line. 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 on the coalescence time of our flows. Then, we study a stochastic differential equation with rank-based coefficients on the plane. The flow solution of this SDE follows from the first SDE. We also study coalescence of this SDE and its kernel solutions.