Accession Number : ADP006618

Title :   A Central Limit Theorem for Extreme Sojourns of Diffusion,

Corporate Author : NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Berman, Stephen M.

Report Date : MAR 1992

Pagination or Media Count : 3

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).

Descriptors :   *RANDOM VARIABLES, *STATISTICAL DISTRIBUTIONS, *STATISTICAL SAMPLES, COEFFICIENTS, CONSTANTS, DIFFUSION, DISTRIBUTION, DRIFT, FUNCTIONS, GENERATORS, STATIONARY, THEOREMS, TIME, VARIABLES.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE