Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142214
Title: Functional inequalities for marked point processes
Authors: Flint, Ian
Privault, Nicolas
Torrisi, Giovanni Luca
Keywords: Science::Mathematics
Issue Date: 2019
Source: Flint, I., Privault, N., & Torrisi, G. L. (2019). Functional inequalities for marked point processes. Electronic Journal of Probability, 24, 116-. doi:10.1214/19-EJP369
Journal: Electronic Journal of Probability
Abstract: In recent years, a number of functional inequalities have been derived for Poisson random measures, with a wide range of applications. In this paper, we prove that such inequalities can be extended to the setting of marked temporal point processes, under mild assumptions on their Papangelou conditional intensity. First, we derive a Poincaré inequality. Second, we prove two transportation cost inequalities. The first one refers to functionals of marked point processes with a Papangelou conditional intensity and is new even in the setting of Poisson random measures. The second one refers to the law of marked temporal point processes with a Papangelou conditional intensity, and extends a related inequality which is known to hold on a general Poisson space. Finally, we provide a variational representation of the Laplace transform of functionals of marked point processes with a Papangelou conditional intensity. The proofs make use of an extension of the Clark-Ocone formula to marked temporal point processes. Our results are shown to apply to classes of renewal, nonlinear Hawkes and Cox point processes.
URI: https://hdl.handle.net/10356/142214
ISSN: 1083-6489
DOI: 10.1214/19-EJP369
Rights: © 2019 The Author(s) (published by The Institute of Mathematical Statistics and the Bernoulli Society). This is an open-access article distributed under the terms of the Creative Commons Attribution License.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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