Non-local Solvable Birth–Death Processes
Keyword(s):
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.
1980 ◽
Vol 24
(2)
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pp. 354-366
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2021 ◽
Vol 2
(3)
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pp. 9-20
2011 ◽
Vol 44
(46)
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pp. 465204
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1981 ◽
pp. 169-212
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