Extreme sojourns of diffusion processes (Q1098498)

Let \(X_ t\) be a diffusion process on an interval. The aim of this paper is to derive limit theorems for the time \(X_ t\) spent above a level u, for u converging to the right inaccessible boundary. Consider the integral of \(J(X_ t)\) up to the passage time of some Z and \(X_ t\) above u. J is a specific function. Asymptotic expressions of this integral are given, which is also approximately J(u) multiplied with the time \(X_ t\) spent above u before hitting z.