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Spectral analysis of bilateral birth-death processes: some new explicit examples (2105.14419v1)
Published 30 May 2021 in math.PR and math.CA
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.
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