Telegraph Process with Elastic Boundary at the Origin

Antonio Di Crescenzo (), Barbara Martinucci () and Shelemyahu Zacks ()
Additional contact information
Antonio Di Crescenzo: Università degli Studi di Salerno
Barbara Martinucci: Università degli Studi di Salerno
Shelemyahu Zacks: Binghamton University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 1, 333-352

Abstract: Abstract We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability α, or reflected upwards, with probability 1−α. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.

Keywords: Finite velocity; Random motion; Telegraph process; Elastic boundary; Absorption time; Renewal cycle; 60K15; 60J25 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-017-9549-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-017-9549-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-017-9549-4

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().