Download ebook Stochastic Processes and Orthogonal Polynomials
Download ebook Stochastic Processes and Orthogonal Polynomials
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Author: W Schoutens
Number of Pages: 184 pages
Published Date: 27 Apr 2000
Publisher: Springer-Verlag New York Inc.
Publication Country: New York, NY, United States
Language: English
ISBN: 9780387950150
Download Link: Stochastic Processes and Orthogonal Polynomials
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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.
Read online Stochastic Processes and Orthogonal Polynomials Buy and read online Stochastic Processes and Orthogonal Polynomials Download Stochastic Processes and Orthogonal Polynomials ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent Download to iPad/iPhone/iOS, B&N nook Stochastic Processes and Orthogonal Polynomials
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Stochastic Processes and Orthogonal Polynomials. W Schoutens
Author: W Schoutens
Number of Pages: 184 pages
Published Date: 27 Apr 2000
Publisher: Springer-Verlag New York Inc.
Publication Country: New York, NY, United States
Language: English
ISBN: 9780387950150
Download Link: 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.
Read online Stochastic Processes and Orthogonal Polynomials Buy and read online Stochastic Processes and Orthogonal Polynomials Download Stochastic Processes and Orthogonal Polynomials ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent Download to iPad/iPhone/iOS, B&N nook Stochastic Processes and Orthogonal Polynomials
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