Bridges with random length: Gamma case

TL;DR

This paper investigates gamma bridges with random length, demonstrating that key properties like the Markov property and canonical decomposition hold, ensuring the filtration's right continuity.

Contribution

It extends known properties of gamma bridges from deterministic to random lengths, confirming their fundamental stochastic characteristics.

Findings

Gamma bridges with random length retain the Markov property.

Canonical decomposition applies to gamma bridges with random length.

The natural filtration of these bridges is right continuous.

Abstract

The aim objective of this paper is to show that certain basic properties of gamma bridges with deterministic length stay true also for gamma bridges with random length. Among them the Markov property as well as the canonical decomposition with respect to the usual augmentation of its natural filtration, which leads us to conclude that its completed natural filtration is right continuous.