Coalescing stochastic flows on the real line (Q921718)

The present paper studies certain stochastic flows of nonsmooth maps known as coalescing flows. Under suitable conditions this paper considers two cases according to whether the infinitesimal correlation function a(x,y) can or cannot be considered as a function of a spatial differential, i.e. the local characteristic has or has not the form b(x- y). Whether coalescence occurs in finite time or not is given by an integral condition for b. Section 2 deals with the construction of stochastic flows and Section 3 states the main theorems for spatially homogeneous flows, while Sections 4, 5 and 6 are concerned with their proofs. The last section considers spatially inhomogeneous flows.