Sojourns and extremes of a diffusion process on a fixed interval
Simeon M. Berman · Advances in Applied Probability · 1982
Let X(t), , be an Ito diffusion process on the real line. For u > 0 and t > 0, let Lt (u) be the Lebesgue measure of the set . Limit theorems are obtained for (i) the distribution of Lt (u) for u → ∞and fixed t, and (ii) the tail of the distribution of the random variable max[0, t] X(s). The conditions on the process are stated in terms of the drift and diffusion coefficients. These conditions imply the existence of a stationary distribution for the process.