Upper first-exit times of compound poisson processes revisited

Autor(en): Stadje, W 
Zacks, S
Stichwörter: Engineering; Engineering, Industrial; M/G/1; Mathematics; Operations Research & Management Science; Statistics & Probability
Erscheinungsdatum: 2003
Herausgeber: CAMBRIDGE UNIV PRESS
Journal: PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES
Volumen: 17
Ausgabe: 4
Startseite: 459
Seitenende: 465
Zusammenfassung: 
For a compound Poisson process (CPP) with only positive jumps, an elegant formula connects the density of the hitting time for a lower straight line with that of the process itself at time t, h (x; t), considered as a function of time and position jointly. We prove an analogous (albeit more complicated) result for the first time the CPP crosses an upper straight line. We also consider the conditional density of the CPP at time t, given that the upper line has not been reached before t. Finally, it is shown how to compute certain moment integrals of h.
ISSN: 02699648
DOI: 10.1017/S0269964803174025

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