Stochastic Processes and Orthogonal Polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2000
|
| Series: | Lecture Notes in Statistics
146 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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. Karlin 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 relationships were developed further. Many birth and death models were related to specific orthogonal polynomials. H. Ogura [87], in 1972, and D. D. Engel [45], in 1982, found an integral relation between the Poisson process and the Charlier polynomials. Some people clearly felt the potential importance 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 differential or difference equation and stresses the limit relations between them |
| Physical Description: | 1 Online-Ressource (XIII, 184p) |
| ISBN: | 9781461211709 9780387950150 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-1170-9 |
Staff View
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| 500 | |a 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. Karlin 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 relationships were developed further. Many birth and death models were related to specific orthogonal polynomials. H. Ogura [87], in 1972, and D. D. Engel [45], in 1982, found an integral relation between the Poisson process and the Charlier polynomials. Some people clearly felt the potential importance 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 differential or difference equation and stresses the limit relations between them | ||
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| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461211709 9780387950150 |
| issn | 0930-0325 |
| language | English |
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| spelling | Schoutens, Wim Verfasser aut Stochastic Processes and Orthogonal Polynomials by Wim Schoutens New York, NY Springer New York 2000 1 Online-Ressource (XIII, 184p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 146 0930-0325 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. Karlin 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 relationships were developed further. Many birth and death models were related to specific orthogonal polynomials. H. Ogura [87], in 1972, and D. D. Engel [45], in 1982, found an integral relation between the Poisson process and the Charlier polynomials. Some people clearly felt the potential importance 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 differential or difference equation and stresses the limit relations between them Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Orthogonale Polynome (DE-588)4172863-4 s 1\p DE-604 Lecture Notes in Statistics 146 (DE-604)BV036592911 146 https://doi.org/10.1007/978-1-4612-1170-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schoutens, Wim Stochastic Processes and Orthogonal Polynomials Lecture Notes in Statistics Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastischer Prozess (DE-588)4057630-9 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4172863-4 |
| title | Stochastic Processes and Orthogonal Polynomials |
| title_auth | Stochastic Processes and Orthogonal Polynomials |
| title_exact_search | Stochastic Processes and Orthogonal Polynomials |
| title_full | Stochastic Processes and Orthogonal Polynomials by Wim Schoutens |
| title_fullStr | Stochastic Processes and Orthogonal Polynomials by Wim Schoutens |
| title_full_unstemmed | Stochastic Processes and Orthogonal Polynomials by Wim Schoutens |
| title_short | Stochastic Processes and Orthogonal Polynomials |
| title_sort | stochastic processes and orthogonal polynomials |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastischer Prozess (DE-588)4057630-9 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastischer Prozess Orthogonale Polynome |
| url | https://doi.org/10.1007/978-1-4612-1170-9 |
| volume_link | (DE-604)BV036592911 |
| work_keys_str_mv | AT schoutenswim stochasticprocessesandorthogonalpolynomials |