THE 3x + 1 PROBLEM: TWO STOCHASTIC MODELS
暂无分享,去创建一个
[1] Charles J. Mode,et al. A general age-dependent branching process. II , 1968 .
[2] R. Azencott,et al. Mélanges d'équations différentielles et grands écarts à la loi des grands nombres , 1977 .
[3] C. J. Everett. Iteration of the number-theoretic function f(2n) = n, f(2n + 1) = 3n + 2 , 1977 .
[4] Richard E. Crandall,et al. On the $‘‘3x+1”$ problem , 1978 .
[5] K. Matthews,et al. A generalization of Hasse's generalization of the Syracuse algorithm , 1984 .
[6] J. Biggins. THE FIRST- AND LAST-BIRTH PROBLEMS FOR A MULTITYPE AGE-DEPENDENT BRANCHING PROCESS , 1976 .
[7] J. Biggins. Chernoff's theorem in the branching random walk , 1977, Journal of Applied Probability.
[8] Daniel A. Rawsthorne. Imitation of an Iteration , 1985 .
[9] J. Kingman. The First Birth Problem for an Age-dependent Branching Process , 1975 .
[10] H. Chernoff. A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .
[11] K. Matthews,et al. A Markov approach to the generalized Syracuse algorithm , 1985 .
[12] Peter Ney,et al. Convexity and Large Deviations , 1984 .
[13] R. Terras,et al. A stopping time problem on the positive integers , 1976 .
[14] Gary T. Leavens. A Distributed Search Program for the 3x + 1 Problem , 1989 .
[15] Kenny S. Crump,et al. An Age-Dependent Branching Process with Correlations Among Sister Cells , 1969 .
[16] Lajos Takács,et al. Combinatorial Methods in the Theory of Stochastic Processes , 1967 .
[17] G. Leigh. A Markov process underlying the generalized Syracuse algorithm , 1986 .
[18] D. Varberg. Convex Functions , 1973 .
[19] R. Terras. On the existence of a density , 1979 .
[20] Jeffrey C. Lagarias,et al. The 3x + 1 Problem and its Generalizations , 1985 .