Estimates for the Syracuse problem via a probabilistic model

Theory of Probability and its Applications

Volumn 45, Issue 2, 2001, Pages 300-310

  Borovkov, K A ^a   Pfeifer, D ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Dynamical system; Random walk; Syracuse problem

Indexed keywords

EID: 0035649630     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97978245     Document Type: Article

References (10)

1. L. S. BLOCK AND W. A. COPPEL, Dynamics in One Dimension, Springer-Verlag, New York, 1992.
2. A. A. BOROVKOV, Stochastic Processes in Queueing Theory, Springer-Verlag, New York, 1976.
3. J. H. CRANDALL, On the "3cursive Greek chi + 1" problem, Math. Comp., 32 (1978), pp. 1281-1292.
4. C. J. EVERETT, Iteration of the number theoretic function f(2n) = n, f(2n + 1) = 3n + 2, Adv. Math., 25 (1977), pp. 42-45.
5. A. GUT, Stopped Random Walks: Limit Theorems and Applications, Springer-Verlag, New York, 1988.
6. J. C. LAGARIAS, The 3cursive Greek chi + 1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), pp. 3-23.
7. J. C. LAGARIAS AND A. WEISS, The 3cursive Greek chi + 1 problem: Two stochastic models, Ann. Appl. Probab., 2 (1992), pp. 229-261.
8. D. SIEGMUND, Sequential Analysis: Tests and Confidence Intervals, Springer-Verlag, New York, 1985.
9. R. TERRAS, A stopping time problem on the positive integers, Acta Arith., 30 (1976), pp. 241-252.
10. R. TERRAS, On the existence of a density, Acta Arith., 35 (1979), pp. 101-102.