On the association and other forms of positive dependence for Feller processes

TL;DR

This paper characterizes various positive dependence structures in jump-Feller processes using their Levy measures and applies these results to several classes of stochastically monotone processes.

Contribution

It provides a novel characterization of positive dependence for jump-Feller processes via Levy measures, extending understanding of dependence in stochastic processes.

Findings

Characterization of association and positive dependence in jump-Feller processes.

Application of results to Levy processes, Ornstein-Uhlenbeck, and subordinated Feller processes.

Insights into dependence structures through Levy measures.

Abstract

We characterize various forms of positive dependence, such as association, positive supermodular association and dependence, and positive orthant dependence, for jump-Feller processes. Such jump processes can be studied through their state-space dependent Levy measures. It is through these Levy measures where we will provide our characterization. Finally, we present applications of these results to stochastically monotone Feller processes, including Levy processes, the Ornstein-Uhlenbeck process, pseudo-Poisson processes, and subordinated Feller processes.