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Stochastic processes with orthogonal polynomial eigenfunctions

โœ Scribed by Bob Griffiths

Book ID
104006660
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
409 KB
Volume
233
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

Markov processes which are reversible with either Gamma, Normal, Poisson or Negative Binomial stationary distributions in the Meixner class and have orthogonal polynomial eigenfunctions are characterized as being processes subordinated to well-known diffusion processes for the Gamma and Normal, and birth and death processes for the Poisson and Negative Binomial. A characterization of Markov processes with Beta stationary distributions and Jacobi polynomial eigenvalues is also discussed.

๐Ÿ“œ SIMILAR VOLUMES

Differential and difference operators ha
Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions
โœ H. Bavinck ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 463 KB

In this paper we consider the polynomials {P~'V(x)}~0, orthogonal with respect to a certain symmetric bilinear form of Sobolev type. These polynomials are the result of two linear perturbations to the orthogonal polynomials {Pn(x)}~0, eigenfunctions of a linear differential or difference operator L.