A Central Limit Theorem for Extreme Sojourns of Diffusion,
Abstract
LetX(t),t >O, be a diffusion process on the real line; and, for be the sojourn time of X(s),O above the level u, that is, the measure of the set The main result is a central limit theorem for the random variable Lt(u), for t and a class of functions u. The conditions in the hypothesis of the theorem are stated in terms of the coefficient functions in the infinitesmal generator of the process, namely, the coefficients of diffusion and drift, denoted as a(x) and b(x), respectively. The conditions that are employed imply, in particular, that there is a stationary proba distribution for this process.' the case of a constant level u, the validity of the central limit theorem was established long ago (Maruyama and Tanaka, 1957).
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1992
- Accession Number
- ADP006618
Entities
People
- Stephen M. Berman
Organizations
- New York University