TITLE

Discrete Compound Poisson Process with Curved Boundaries: Polynomial Structures and Recursions

AUTHOR(S)
Lefèvre, Claude
PUB. DATE
June 2007
SOURCE
Methodology & Computing in Applied Probability;Jun2007, Vol. 9 Issue 2, p243
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This paper provides a review of recent results, most of them published jointly with Ph. Picard, on the exact distribution of the first crossing of a Poisson or discrete compound Poisson process through a given nondecreasing boundary, of curved or linear shape. The key point consists in using an underlying polynomial structure to describe the distribution, the polynomials being of generalized Appell type for an upper boundary and of generalized Abel–Gontcharoff type for a lower boundary. That property allows us to obtain simple and efficient recursions for the numerical determination of the distribution.
ACCESSION #
24942843

 

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