[Statlist] Séminaire 26/06/2007 - Institut de Statistique, Neuchâtel

[ISTAT Messagerie]

S�minaire de Statistique 
Institut de Statistique, Universit� de Neuch�tel 

Pierre � Mazel 7 (1er �tage,salle 110), Neuch�tel,

http://www2.unine.ch/statistics

Mardi 26 juin 2007, 11h00

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Prof. P.R. Parthasarathy

Department of Mathematics,  Indian Institute of Technology, Madras

 

Topic: Exact Transient Solution of a State-dependent Birth and Death Process.

 

Abstract: The time-dependent solution of certain simple birth and death processes are usually derived by solving partial differential equations satisfied by the generating functions. In this talk, we obtain the transient probabilities of state-dependent birth and death processes in terms of power series expression using continued fractions. In this study, the underlying forward Kolmogorov differential-difference equations are first transformed into a set of linear algebraic equations by employing Laplace transforms. This leads to a J-fraction which is expressed as a formal power series. Inverting we get the transient probabilities of state-dependent BDPs in closed form. Several examples are presented to illustrate this approach.

 


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