Association and other forms of positive dependence for Feller evolution systems

TL;DR

This paper characterizes various forms of positive dependence in Feller evolution processes and jump-FEPs using their generators and Levy measures, with applications to financial modeling.

Contribution

It introduces a framework to analyze positive dependence in time-inhomogeneous Markov processes via their generators and Levy measures, extending previous work.

Findings

Characterization of positive dependence for FEPs and jump-FEPs.

Application of results to additive processes in finance.

Use of generators and Levy measures for dependence analysis.

Abstract

We characterize various forms of positive dependence for a general class of time-inhomogeneous Markov processes called Feller evolution processes (FEPs) and for jump-FEPs. General FEPs can be studied through their time and state-space dependent (extended) generators. We will use the time and state-space dependent (extended) generators and time and state-space dependent Levy measures to characterize the positive dependence of general FEPs and jump-FEPs, respectively. Finally, we present applications of these results to additive processes, which are time-inhomogeneous Levy processes, often arising as useful examples in financial modeling.