{"product_id":"stochastic-processes-and-orthogonal-polynomials-lecture-notes-in-statistics-146-038795015x","title":"Stochastic Processes and Orthogonal Polynomials (Lecture Notes in Statistics, 146)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 038795015X\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Schoutens, Wim\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\u003cp\u003eIt 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.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51824201007392,"sku":"NEW038795015X","price":70.8,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/61Zt-LTKHEL.jpg?v=1781209274","url":"https:\/\/miakarts.com\/products\/stochastic-processes-and-orthogonal-polynomials-lecture-notes-in-statistics-146-038795015x","provider":"Miakarts Books","version":"1.0","type":"link"}