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

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

Antonio Di Crescenzo* email and Barbara Martinucciemail
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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Abstract: 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

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Cite This Article

MDPI and ACS Style

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

AMA Style

Di Crescenzo A, Martinucci B. On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities. Symmetry. 2009; 1(2):201-214.

Chicago/Turabian Style

Di Crescenzo, Antonio; Martinucci, Barbara. 2009. "On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities." Symmetry 1, no. 2: 201-214.

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