Pacific Journal of Mathematics

Random walks and Riesz kernels.

J. A. Williamson

Article information

Source
Pacific J. Math., Volume 25, Number 2 (1968), 393-415.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102986279

Mathematical Reviews number (MathSciNet)
MR0226741

Zentralblatt MATH identifier
0239.60066

Subjects
Primary: 60.66

Citation

Williamson, J. A. Random walks and Riesz kernels. Pacific J. Math. 25 (1968), no. 2, 393--415. https://projecteuclid.org/euclid.pjm/1102986279


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References

  • [1] N. G. deBruijn and P. Erdos, On a recursion formula and some Tauberian theorems, J. Res. Nat. Bur. Stand. 50 (1953), 161-164.
  • [2] R. A. Doney, An analogue of the renewal theorem in higher dimensions, Proc. of London Math. Soc, Clarendon Press, Oxford, 1966, 669-684.
  • [3] J. L. Doob, Discrete potential theory and boundaries, J. Math, and Mech. 8 (1959), 433-458.
  • [4] J. L. Doob, J. L. Snell and R. E. Williamson, Application of boundary theory to sums of independentrandom variables, Contributions to probability and statistics, Stanford University Press, Stanford, California, 1960, 182-197.
  • [5] A. Garsia and J. Lamperti, A discrete renewal theorem with infinitemean, Com- mentarii Mathematici Helvetic! 37 (1963), 221-234.
  • [6] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, Mass., 1954.
  • [7] G. A. Hunt, Markov chains and Martin boundaries, Illinois J. Math. 4 (1960), 313- 340.
  • [8] H. J. Karamata, Sur un mode de croissance reguliere, Bull. Soc. Math, de France 61 (1933), 55-62.
  • [9] J. Lamperti, Wiener's test and Markov chains, J. of Math. Analysis and Appli- cations 6 (1963), 58-66.
  • [10] P. Levy, Theorie de Vaddition des variables aleatoires, Gauthier-Villars, Paris, 1937.
  • [11] P. Ney and F. Spitzer, The Martin boundary for random walk, Trans. Amer. Math. Soc. 121 (1966), 116-132.
  • [12] S. C. Port, Hitting times for transient stable processes, J. Math, and Mech. 16 (1967), 1229-1246.
  • [13] G. S. Rinehart and J. A. Williamson, Remarks on the periodic behavior in time of sums of random variables (to appear)
  • [14] E. L. Rvaceva, On domains of attractionof multi-dimensionaldistributions, Selected Translations in Mathematical Statistics and Probability II (1962), 183-205. L'vov. Gos. Univ. Uc. Zap. 29 Ser. Meh.-Mat. 6 (1954), 5-44.
  • [15] A. V. Skorohod, Asymptotic formulas for stable distribution laws, Selected Trans- lations in Mathematical Statistics and Probability I (1961), 157-161.Dokl. Akad. Nauk SSSR. 98 (1954), 731-734.
  • [16] F. Spitzer, Principles of Random Walk,, Van Nostrand, Princeton, N. J., 1964.
  • [17] S. J. Taylor, Sample path properties of a transient stable process, Pacific J. Math. 21 (1967), 161-165.
  • [18] A. Zygmund, Trigonometrical Series, Chelsea. 1952.