LETTER TO THE EDITOR: Partial survival and crossing statistics for a diffusing particle in a transverse shear flow

We consider a non-Gaussian stochastic process where a particle diffuses in the y-direction, dy/dt = η(t), subject to a transverse shear flow in the x-direction, dx/dt = f(y). Absorption with probability p occurs at each crossing of the line x = 0. We treat the class of models defined by f(y) = ±ν ± (±y) α where the upper (lower) sign refers to y > 0 (y < 0). We show that the particle survives up to time t with probability Q(t) ∼ t -θ(p) and we derive an explicit expression for 0(p) in terms of a and the ratio v + /v - . From θ(p) we deduce the mean and variance of the density of crossings of the line x = 0 for this class of non-Gaussian processes.