Spectral analysis of bilateral birth-death processes: some new explicit examples

2021/05/30 by de la Iglesia, Manuel D.
#33C45 #42C05 #60J27 #60J80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2105.14419

Abstract

We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, like recurrence, the invariant distribution (if it exists) or the probability current.

Related

• On some transformations of bilateral birth-and-death processes with applications
• Quasi-birth-and-death processes and multivariate orthogonal polynomials
• Birth-Death processes with two-type catastrophes
• The bilateral birth-death chain generated by the associated Jacobi polynomials
• Intertwining of birth-and-death processes