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The Hawkins sieve and Brownian motion. (English) Zbl 0402.10052


MSC:

11K99 Probabilistic theory: distribution modulo \(1\); metric theory of algorithms
11N35 Sieves
60F99 Limit theorems in probability theory
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References:

[1] D. Freedman : Brownian Motion and Diffusion (Holden-Day, San Francisco, 1971). · Zbl 0231.60072
[2] D.G. Kendall : Branching processes since 1873 , J. London Math. Soc. 41 (1966) 385-406. · Zbl 0154.42505 · doi:10.1112/jlms/s1-41.1.385
[3] M. Loéve : Probability Theory (van Nostrand, Princeton, N.J., 1963). · Zbl 0108.14202
[4] H.P. Mckean : Stochastic Integrals (Academic Press, New York-London, 1969). · Zbl 0191.46603
[5] W. Neudecker and D. Williams : The ’Riemann hypothesis’ for the Hawkins random sieve , Compositio Math. 29 (1974) 197-200. · Zbl 0312.10033
[6] M. Pinsky : Differential equations with a small parameter and the central limit theorem for functions defined on a Markov chain , Z. Wahrscheinlichkeitstheorie 9 (1968) 101-111. · Zbl 0155.24203 · doi:10.1007/BF01851001
[7] V. Strassen : Almost sure behavior of sums of independent random variables and martingales , Proc. 5th Berkeley Symp., Vol. 2, part 1 (1966) 315-343. · Zbl 0201.49903
[8] D.W. Stroock : Two limit theorems for random evolutions having non-ergodic driving processes , (to appear in proceedings of Park City, Utah conference on stochastic differential equations). · Zbl 0463.60052
[9] D. Williams : A study of a diffusion process motivated by the sieve of Eratosthenes , Bull. London Math. Soc. 6 (1974) 155-164. · Zbl 0326.60094 · doi:10.1112/blms/6.2.155
[10] M.C. Wunderlich : The prime number theorem for random sequences , J. Number Theory 8 (1976) 369-371. · Zbl 0341.10036 · doi:10.1016/0022-314X(76)90084-6
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