Stochastic Processes and Orthogonal Polynomials
(Sprache: Englisch)
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...
Leider schon ausverkauft
versandkostenfrei
Buch (Kartoniert)
106.99 €
Produktdetails
Produktinformationen zu „Stochastic Processes and Orthogonal Polynomials “
Klappentext zu „Stochastic Processes and Orthogonal Polynomials “
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.
Inhaltsverzeichnis zu „Stochastic Processes and Orthogonal Polynomials “
- The Askey-Scheme of Orthogonal Polynomials- Stochastic Processes
- Birth and Death Processes and Orthogonal Polynomials
- Random Walks and Orthogonal Polynomials
- Sheffer Systems
- Orthogonal Polynomials in Stochastic Integration Theory
- Chaotic and Previsible Representations for Lvy Processes
- Stein Approximation and Orthogonal Polynomials
Bibliographische Angaben
- Autor: Wim Schoutens
- 2000, XIII, 184 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 038795015X
- ISBN-13: 9780387950150
- Erscheinungsdatum: 27.04.2000
Sprache:
Englisch
Kommentar zu "Stochastic Processes and Orthogonal Polynomials"
0 Gebrauchte Artikel zu „Stochastic Processes and Orthogonal Polynomials“
Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
---|
Schreiben Sie einen Kommentar zu "Stochastic Processes and Orthogonal Polynomials".
Kommentar verfassen