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Stochastic Processes and Orthogonal Polynomials

Jezik EngleskiEngleski
Knjiga Meki uvez
Knjiga Stochastic Processes and Orthogonal Polynomials Wim Schoutens
Libristo kod: 06793818
Nakladnici Springer-Verlag New York Inc., travanj 2000
It has been known for a long time that there is a close connection between stochastic processes and... Cijeli opis
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It has been known for a long time that there is a close connection between stochastic processes and orthogonal polynomials. For example, N. Wiener [112] and K. Ito [56] knew that Hermite polynomials play an important role in the integration theory with respect to Brownian motion. In the 1950s D. G. Kendall [66], W. Ledermann and G. E. H. Reuter [67] [74], and S. Kar lin and J. L. McGregor [59] established another important connection. They expressed the transition probabilities of a birth and death process by means of a spectral representation, the so-called Karlin-McGregor representation, in terms of orthogonal polynomials. In the following years these relation ships were developed further. Many birth and death models were related to specific orthogonal polynomials. H. Ogura [87], in 1972, and D. D. En gel [45], in 1982, found an integral relation between the Poisson process and the Charlier polynomials. Some people clearly felt the potential im portance of orthogonal polynomials in probability theory. For example, P. Diaconis and S. Zabell [29] related Stein equations for some well-known distributions, including Pearson's class, with the corresponding orthogonal polynomials. The most important orthogonal polynomials are brought together in the so-called Askey scheme of orthogonal polynomials. This scheme classifies the hypergeometric orthogonal polynomials that satisfy some type of differ ential or difference equation and stresses the limit relations between them.

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Informacije o knjizi

Puni naziv Stochastic Processes and Orthogonal Polynomials
Autor Wim Schoutens
Jezik Engleski
Uvez Knjiga - Meki uvez
Datum izdanja 2000
Broj stranica 184
EAN 9780387950150
ISBN 038795015X
Libristo kod 06793818
Nakladnici Springer-Verlag New York Inc.
Težina 590
Dimenzije 155 x 235 x 11

Kategorija

Mathematics & Science > Mathematics > Applied mathematics > Stochastics
Reference, Information & Interdisciplinary subjects > Encyclopaedias & reference works > Reference works
Mathematics & Science > Mathematics > Probability & statistics
Medicine & Nursing > Medicine: general issues
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