On point measures of [var epsilon]-upcrossings for stationary diffusions

Bronius Grigelionis

Statistics & Probability Letters, 2003, vol. 61, issue 4, 403-410

Abstract: We consider ergodic strictly stationary diffusion processes on an open interval (l,r)[subset, double equals]R1 with a predetermined stationary distribution H, named H-diffusions. Simple sufficient conditions for vague convergence of the time-normalized point measures of [var epsilon]-upcrossings of an H-diffusion to the Poisson measure are derived from the general result by Borkovec and Klüppelberg (Extremes 1(1) (1998) 47) in the terms of the stationary density and the scale function, describing an H-diffusion. Some examples are discussed in detail.

Keywords: Ergodic; diffusion; process; H-diffusions; Extreme; value; theory; Point; measures; of; [var; epsilon]-upcrossings; Poisson; point; measure (search for similar items in EconPapers)
Date: 2003
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