Work

On the distribution of the telegraph meander and its properties

Year: 2026

Type: article

Abstract: In this paper we study the telegraph meander, a random function obtained by conditioning the telegraph process to stay above the zero level. The finite dimensional distribution of the telegraph meander is derived by applying the reflection principle for the telegraph process and the Markovianity of the telegraph process with the velocity process. We show that the law of the telegraph meander at the end time is a solution to a hyperbolic equation, and we find the characteristic function and moments of any order. Finally, we prove that Brownian meander is the weak limit of the telegraph meander.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2026.104887

Authors: A. Pedicone, E. Orsingher

Institution: Sapienza University of Rome

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

OpenAlex ID: W7124213859

FWCI:

Cites: 21

Cited by:

Related to: