Conditioned Point Processes with Application to Lévy Bridges

Giovanni Conforti (), Tetiana Kosenkova () and Sylvie Rœlly ()
Additional contact information
Giovanni Conforti: Université Paris-Saclay
Tetiana Kosenkova: Institut für Mathematik der Universität Potsdam
Sylvie Rœlly: Institut für Mathematik der Universität Potsdam

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 2111-2134

Abstract: Abstract Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke’s formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump Lévy process in $$\mathbb {R}^d$$ R d with a height $$\mathfrak {a}$$ a can be interpreted as a Poisson point process on space–time conditioned by pinning its first moment to $$\mathfrak {a}$$ a , our approach allows us to characterize bridges of Lévy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample Lévy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein–Uhlenbeck processes driven by Lévy noise.

Keywords: Conditioned point processes; Mecke’s formula; Lévy bridges; Periodic Ornstein–Uhlenbeck; 60G51; 60G55 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-018-0863-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0863-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-018-0863-8

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().