How many random walks correspond to a given set of return probabilities to the origin?

Stochastic Processes and their Applications

Volumn 64, Issue 1, 1996, Pages 17-30

  Dette, Holger ^a   Studden, William J ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Chain sequences; Continued fractions; Random walks

Indexed keywords

EID: 0030295795     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(96)00083-X     Document Type: Article

References (9)

1. T.S. Chihara, An Introduction to Orthogonal Polynomials (Gordon and Breach, New York, 1978).
2. H. Dette and W.J. Studden, Theory of canonical moments with applications in statistics, probability and analysis (Wiley, New York), (1996) forthcoming.
3. P. Flajolet, Combinatorical aspects of continued fractions, Discrete Math. 32 (1980) 125-162.
4. I.J. Good, Random motion and analytic continued fractions, Proc. Camb. Phil. Soc. 54 (1958) 43-47.
5. S. Karlin and J. McGregor, Random walks, I1. J. Math. 3 (1959) 66-81.
6. M. Skibinsky, Principal representations and canonical moment sequences for distributions on an interval, J. Math. Anal. Appl. 120 (1986) 95-120.
7. E.A. Van Doorn and P. Schrijner, Random walk polynomials and random walk measures, J. Comput. Appl. Math. 49 (1993) 289-296.
8. H.S. Wall, Analytic Theory of Continued Fractions (Van Nostrand, New York, 1948).
9. T.A. Whitehurst, An application of orthogonal polynomials to random walks, Pacific J. Math. 99 (1982) 205-213.