{ "item_title" : "Stochastic Processes and Orthogonal Polynomials", "item_author" : [" Wim Schoutens "], "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. Wiener112] and K. Ito56] knew that Hermite polynomials play an important role in the integration theory with respect to Brownian motion. In the 1950s D. G. Kendall66], W. Ledermann and G. E. H. Reuter67]74], and S. Kar- lin and J. L. McGregor59] 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. Ogura87], in 1972, and D. D. En- gel45], 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. Zabell29] 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.", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/0/38/795/015/038795015X_b.jpg", "price_data" : { "retail_price" : "109.99", "online_price" : "109.99", "our_price" : "109.99", "club_price" : "109.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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