Random walk polynomials and random walk measures
Doorn, Erik A. van and Schrijner, Pauline (1993) Random walk polynomials and random walk measures. Journal of Computational and Applied Mathematics, 49 (13). pp. 289296. ISSN 03770427

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Abstract:  Random walk polynomials and random walk measures play a prominent role in the analysis of a class of Markov chains called random walks. Without any reference to random walks, however, a random walk polynomial sequence can be defined (and will be defined in this paper) as a polynomial sequence which is orthogonal with respect to a measure on [1, 1] and which is such that the parameters (alfa)n in the recurrence relations Pn=1(x)=(x(alfa)n)Pn(x)ßnPn1(x) are nonnegative. Any measure with respect to which a random walk polynomial sequence is orthogonal is a random walk measure. We collect some properties of random walk measures and polynomials, and use these findings to obtain a limit theorem for random walk measures which is of interest in the study of random walks. We conclude with a conjecture on random walk measures involving 
Item Type:  Article 
Copyright:  © 1993 Elsevier Science 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/30032 
Official URL:  http://dx.doi.org/10.1016/03770427(93)901625 
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