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On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities
Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy
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Received: 23 October 2009 / Accepted: 24 November 2009 / Published: 26 November 2009
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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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.
Di Crescenzo A, Martinucci B. On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities. Symmetry. 2009; 1(2):201-214.
Di Crescenzo, Antonio; Martinucci, Barbara. 2009. "On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities." Symmetry 1, no. 2: 201-214.