Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 3, 324-344

ON A UNIFORM RANDOM WALK CONDITIONED TO STAY POSITIVE

By

WOLFGANG STADJE, Universität Osnabrück

SUMMARY. For arbitrary N, M Î N we consider the 'uniform random walk' (Sn )n ³ 0 with step sizes -N, -N+1, ., 0,. , M and S0 = a Î N, conditioned to stay positive. The conditional generating functions of S0, S1 ,S2 ,. Are expressed in terms of the coefficients of expansion of the function PN+M (x)n, where Pi(x) = 1+ x ++ xi (i Î N), in ascending powers of x or, for M = 1, using alternatively the inverse function of x/PN+1(x), thereby avoiding infinite series. In the skipfree case M = 1 or N = 1 the conditional distribution of Sn is explicitly given in terms of these coefficients.

 

AMS (1991) subject classification. 62F15, 62C10

Key words and phrases. Bayes factor, double exponential model, influential observation, intrinsic Bayes factor, Jefferys' prior, Laplace method, noninformative prior, posterior Bayes factor

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