H.K. Hwang, A constant arising from the analysis of algorithms for determining the maximum of a random walk, R.S.A. Vol. 10 p. 333-335, (1997).

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An Average Case Quasi Optimal Search Algorithm for the Zeros of.. - Marckert   (Correct)

....k such that S k = p n For related results, one can see Odlyzko [8] who studied the search of the maximum of random walks with n steps, in the symmetric case. He proved that on average c p n o( p n) probes are necessary and sucient to nd the maximum, where c = p 8= log 2 (Hwang [5] and Chassaing [2] In the asymmetric case, Chassaing [2] proved that only log n= j log(p) log(1 p)j) probes are necessary and sucient on average (where P(X i = 1) 1 P(X i = 1) p 6= 1 2 ) 2 2 The double jump algorithm 2.1 Preliminaries Let us rst prove the existence of a large ....

H.K. Hwang, A constant arising from the analysis of algorithms for determining the maximum of a random walk, R.S.A. Vol. 10 p. 333-335, (1997).

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