Random walk polynomials and random walk measures

Doorn van, Erik A. and Schrijner, Pauline (1993) Random walk polynomials and random walk measures. Journal of Computational and Applied Mathematics, 49 (1-3). pp. 289-296. ISSN 0377-0427

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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 ${Pn(x)}$ 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)-ßnPn-1(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)
Research Group:	Statistics and Probability (SP)
Link to this item:	http://purl.utwente.nl/publications/30032
Official URL:	http://dx.doi.org/10.1016/0377-0427(93)90162-5
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