Abstract
AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
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