Approximations for compound Poisson and Pólya processes

Suppose Xi ≧0 are i.i.d., i = 1, 2, ···. We derive a saddlepoint approximation for P{∑N(t) k=1 X k> y} as y→∞ and t is fixed, where N(t), t≧0, is either a Poisson or a Pólya process. These results are then compared and contrasted with the well-known Esscher approximation.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Advances in applied probability 1985-09, Vol.17 (3), p.623-637
Hauptverfasser:	Embrechts, Paul, Jensen, Jens L., Maejima, Makoto, Teugels, J. L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation College mathematics Eigenfunctions Exact sciences and technology Generating function Laplace transformation Mathematics Perceptron convergence procedure Poisson process Probability and statistics Probability theory Probability theory and stochastic processes Radii of convergence Random variables Sciences and techniques of general use Stochastic analysis
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Suppose Xi ≧0 are i.i.d., i = 1, 2, ···. We derive a saddlepoint approximation for P{∑N(t) k=1 X k> y} as y→∞ and t is fixed, where N(t), t≧0, is either a Poisson or a Pólya process. These results are then compared and contrasted with the well-known Esscher approximation.
ISSN:	0001-8678 1475-6064
DOI:	10.2307/1427123