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Symmetry 2009, 1(2), 201-214; doi:10.3390/sym1020201

On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities

*  and
Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy
* Author to whom correspondence should be addressed.
Received: 23 October 2009 / Accepted: 24 November 2009 / Published: 26 November 2009
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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We consider a bilateral birth-death process having sigmoidal-type rates. A thorough discussion on its transient behaviour is given, which includes studying symmetry properties of the transition probabilities, finding conditions leading to their bimodality, determining mean and variance of the process, and analyzing absorption problems in the presence of 1 or 2 boundaries. In particular, thanks to the symmetry properties we obtain the avoiding transition probabilities in the presence of a pair of absorbing boundaries, expressed as a series.
Keywords: bilateral processes; transition probabilities; first-passage-time; absorption bilateral processes; transition probabilities; first-passage-time; absorption
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Di Crescenzo, A.; Martinucci, B. On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities. Symmetry 2009, 1, 201-214.

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