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An application of
orthogonal polynomials to random walks
Thomas Alva Whitehurst |
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Vol. 99 (1982), No. 1, 205–213
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Abstract |
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If Xn is a simple random walk on the nonnegative integers with transition probabilities Pij(k) = Pr{Xn+k = j∣Xn = i}, then Pij(k) has an integral representation in terms of a family of orthogonal polynomials and the associated probability distribution function F(x) for these polynomials. The relationship between the distribution F, the family of polynomials and the random walk Xn is studied. Necessary and sufficient conditions for the support of F to be contained in [0,1] are given. |
Mathematical Subject Classification 2000
Primary: 60J15
Secondary: 60J10
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Milestones
Received: 4 February 1980
Published: 1 March 1982
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Authors |
| Thomas Alva Whitehurst | |
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