Strangely sweeping one-dimensional diffusion
Volume 58 / 1993
Annales Polonici Mathematici 58 (1993), 37-45
DOI: 10.4064/ap-58-1-37-45
Abstract
Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = Prob{X(t) ≥ 0} as t → ∞ and construct an equation such that $lim sup_{t→∞} t^{-1} ∫_0^t p(s) ds = 1$ and $lim inf_{t→∞}t^{-1} ∫_0^t p(s) ds = 0$.
