Distribution of Overjump Functionals of a Semicontinuous Homogeneous Process with Independent Increments

Authors

  • D. V. Gusak

Abstract

We establish relations for the distributions of functionals associated with an overjump of a process ξ(t) with continuously distributed jumps of arbitrary sign across a fixed level x > 0 (including the zero level x = 0 and infinitely remote level x → ∞). We improve these relations in the case where the distributions of maxima and minima of ξ(t) may have an atom at zero. The distributions of absolute extrema of semicontinuous processes are defined in terms of these atomic probabilities and the cumulants of the corresponding monotone processes.

Published

25.03.2002

Issue

Section

Research articles

How to Cite

Gusak, D. V. “Distribution of Overjump Functionals of a Semicontinuous Homogeneous Process With Independent Increments”. Ukrains’kyi Matematychnyi Zhurnal, vol. 54, no. 3, Mar. 2002, pp. 303-21, https://umj.imath.kiev.ua/index.php/umj/article/view/4067.