Translator Disclaimer
December 2015 Laplace transform identities for the volume of stopping sets based on Poisson point processes
Nicolas Privault
Author Affiliations +
Adv. in Appl. Probab. 47(4): 919-933 (December 2015). DOI: 10.1239/aap/1449859794

Abstract

We derive Laplace transform identities for the volume content of random stopping sets based on Poisson point processes. Our results are based on anticipating Girsanov identities for Poisson point processes under a cyclic vanishing condition for a finite difference gradient. This approach does not require classical assumptions based on set-indexed martingales and the (partial) ordering of index sets. The examples treated focus on stopping sets in finite volume, and include the random missed volume of Poisson convex hulls.

Citation

Download Citation

Nicolas Privault. "Laplace transform identities for the volume of stopping sets based on Poisson point processes." Adv. in Appl. Probab. 47 (4) 919 - 933, December 2015. https://doi.org/10.1239/aap/1449859794

Information

Published: December 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1366.60075
MathSciNet: MR3433290
Digital Object Identifier: 10.1239/aap/1449859794

Subjects:
Primary: 60D05
Secondary: 60G40 , 60G48 , 60G57 , 60H07

Keywords: anticipating stochastic calculus , gamma-type distribution , Girsanov identity , Poisson point process , stopping set

Rights: Copyright © 2015 Applied Probability Trust

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 4 • December 2015
Back to Top