L\'evy bridges with random length

TL;DR

This paper defines Levy bridges with random length and proves their Markov property, which is essential for understanding their filtration and continuity properties in stochastic processes.

Contribution

It introduces a precise definition of Levy bridges with random length and establishes their Markov property relative to their natural filtration.

Findings

Defined Levy bridges with random length.

Proved Markov property of these processes.

Ensured right-continuity of the filtration.

Abstract

In this paper our first goal is to give precise definition of the L\'evy bridges with random length. Our second task is to establish the Markov property of this process with respect to its completed natural filtration and thus with respect to the usual augmentation of this one. This property will be crucial for the right-continuity of completed natural filtration.