Partial Survival and Crossing Statistics for a Diffusing Particle in a Transverse Shear Flow

Abstract

We consider a non-Gaussian stochastic process where a particle diffuses in the $y$-direction, $dy/dt=\eta (t)$, 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 $f(y)=\pm v_{\pm }(\pm y{)}^{\alpha }$ where the upper (lower) sign refers to $y>0$ ($y<0$). We show that the particle survives up to time $t$ with probability $Q(t)\sim t^{-\theta (p)}$ and we derive an explicit expression for $\theta (p)$ in terms of $\alpha$ and the ratio $v_{+}/v_{-}$. From $\theta (p)$ we deduce the mean and variance of the density of crossings of the line $x=0$ for this class of non-Gaussian processes.

4 pages

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Cited by in corpus (3)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Persistence of a Rouse polymer chain under transverse shear flow
• Time correlations and persistence probability of a Brownian particle in a shear flow