The Hawkins sieve and brownian motion

Dorothy Foster; David Williams

Compositio Mathematica (1978)

  • Volume: 37, Issue: 3, page 277-289
  • ISSN: 0010-437X

How to cite


Foster, Dorothy, and Williams, David. "The Hawkins sieve and brownian motion." Compositio Mathematica 37.3 (1978): 277-289. <>.

author = {Foster, Dorothy, Williams, David},
journal = {Compositio Mathematica},
keywords = {Hawkins Sieve; Riemann Hypothesis; Sample Space; Brownian Motion; Diffusion; Martingales},
language = {eng},
number = {3},
pages = {277-289},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {The Hawkins sieve and brownian motion},
url = {},
volume = {37},
year = {1978},

AU - Foster, Dorothy
AU - Williams, David
TI - The Hawkins sieve and brownian motion
JO - Compositio Mathematica
PY - 1978
PB - Sijthoff et Noordhoff International Publishers
VL - 37
IS - 3
SP - 277
EP - 289
LA - eng
KW - Hawkins Sieve; Riemann Hypothesis; Sample Space; Brownian Motion; Diffusion; Martingales
UR -
ER -


  1. [1] D. Freedman: Brownian Motion and Diffusion (Holden-Day, San Francisco, 1971). Zbl0231.60072MR297016
  2. [2] D.G. Kendall: Branching processes since 1873, J. London Math. Soc.41 (1966) 385-406. Zbl0154.42505MR198551
  3. [3] M. Loéve: Probability Theory (van Nostrand, Princeton, N.J., 1963). Zbl0108.14202MR203748
  4. [4] H.P. McKean: Stochastic Integrals (Academic Press, New York-London, 1969). Zbl0191.46603MR247684
  5. [5] W. Neudecker and D. Williams: The 'Riemann hypothesis' for the Hawkins random sieve, Compositio Math.29 (1974) 197-200. Zbl0312.10033MR399029
  6. [6] M. Pinsky: Differential equations with a small parameter and the central limit theorem for functions defined on a Markov chain, Z. Wahrscheinlichkeitstheorie9 (1968) 101-111. Zbl0155.24203MR228067
  7. [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. Zbl0201.49903MR214118
  8. [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). Zbl0463.60052
  9. [9] D. Williams: A study of a diffusion process motivated by the sieve of Eratosthenes, Bull. London Math. Soc.6 (1974) 155-164. Zbl0326.60094MR359027
  10. [10] M.C. Wunderlich: The prime number theorem for random sequences, J. Number Theory8 (1976) 369-371. Zbl0341.10036MR429799

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