Year: 2024
Type: preprint
Abstract: This paper is interested in proving correlation inequalities of the FKG-type for various stochastic processes in continuous time. The pivotal tool which yields these correlation inequalities is an approximation with (possibly conditioned) Markov chains and random walks. In particular, we prove FKG inequalities for Lévy processes, Bessel processes and several conditioned Brownian processes. As a side result, we also provide a necessary and sufficient condition for a random walk distribution in $\bbZ$ to satisfy the well-known ``FKG lattice condition''.
Source: arXiv (Cornell University)
Author: Legrand, Alexandre
Institutions: Lyon 1 Université, Institut Camille Jordan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4402855161