Probability Commons^™

Dependence Structures In Lévy-Type Markov Processes, Eddie Brendan Tu

Doctoral Dissertations

In this dissertation, we examine the positive and negative dependence of infinitely divisible distributions and Lévy-type Markov processes. Examples of infinitely divisible distributions include Poissonian distributions like compound Poisson and α-stable distributions. Examples of Lévy-type Markov processes include Lévy processes and Feller processes, which include a class of jump-diffusions, certain stochastic differential equations with Lévy noise, and subordinated Markov processes. Other examples of Lévy-type Markov processes are time-inhomogeneous Feller evolution systems (FES), which include additive processes. We will provide a tour of various forms of positive dependence, which include association, positive supermodular association (PSA), positive supermodular dependence (PSD), and positive …