On the continuous dual Hahn process

TL;DR

This paper extends the continuous dual Hahn process to the entire real line by taking a limit of a related Markov process and characterizes it through conditional means and variances.

Contribution

It introduces a novel extension of the continuous dual Hahn process to the real line and provides a characterization via conditional moments.

Findings

Extended the process to the entire real line.

Characterized the process through conditional means and variances.

Provided a limit construction from related Markov processes.

Abstract

In this note we extend the continuous dual Hahn process constructed by Corwin and Knizel on a finite time interval to the entire real line by taking a limit of a closely related Markov process. We also characterize this Markov processes by conditional means and variances under bidirectional conditioning.