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Arithmetic simulation of stochastic processes

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Literature Cited

  1. P. Billingsley, Convergence of Probability Measures, Wiley (1968).

  2. I. P. Kubilyus, Probabilistic Methods in Number Theory [in Russian], Gos. Izd. Polit. Nauchn. Lit. LitSSR, Vilnius (1962).

    Google Scholar 

  3. J. Kubilius, “Additive arithmetic functions and Brownian motion,” Lect. Notes Math.,550, 335–350 (1976).

    Google Scholar 

  4. P. Billingsley, “Additive functions and Brownian motion,” Not. Am. Math. Soc.,17, 1050 (1970).

    Google Scholar 

  5. P. Billingsley, “Prime numbers and Brownian motion,” Am. Math. Monthly,80, 1099–1115 (1973).

    Google Scholar 

  6. P. Billingsley, “The probability theory of additive arithmetic functions,” Ann. Probab., No. 2, 749–791 (1974).

    Google Scholar 

  7. W. Philipp, “Arithmetic functions and Brownian motion,” Proc. Sympos. Pure Math.,24, 233–246 (1973).

    Google Scholar 

  8. G. J. Babu, “Probabilistic methods in the theory of additive arithmetic functions,” Ph. D. Dissertation. The Indian Statistical Institute, Calcutta (1973).

    Google Scholar 

  9. N. M. Timofeev and Kh. Kh. Usmanov, “Additive functions and limit theorems in function spaces,” Izv. Akad. Nauk TadzhSSR, Otd. Fiz.-Mat. Geol.-Khim. Nauk,70, No. 4, 25–33 (1978).

    Google Scholar 

  10. N. M. Timofeev and Kh. Kh. Usmanov, “Arithmetic simulation of Brownian motion,” Dokl. Akad. Nauk TadzhSSR,25, No. 4, 207–211 (1982).

    Google Scholar 

  11. E. Manstavicyus, “Probabilistic number theory,” Liet. Mat. Rinkinys,20, No. 3, 39–52 (1980).

    Google Scholar 

  12. E. Manstavichyus, “Irrationality and stable processes,” in: Abstracts of Reports to the Conference “Theory of Transcendental Numbers and Its Applications” [in Russian], Moscow (1983), pp. 84–85.

  13. A. A. Borovkov, “Rate of convergence in the invariance principle,” Teor. Veroyatn. Primen.,18, No. 2, 217–234 (1973).

    Google Scholar 

  14. I. Z. Ruzsa, “Generalized moments of additive functions,” J. Number Theory (1984) (in press).

  15. I. Z. Ruzsa, “Effective results in probabilistic number theory,” Preprint No. 12/1982, Budapest.

  16. A. V. Skorokhod, Stochastic Processes and Independent Increments [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  17. A. I. Sakhanenko, “Estimates of rate of convergence in the invariance principle,” Tr. Inst. Mat. Akad. Nauk SSSR, Sib. Otd.,1, 72–78 (1982).

    Google Scholar 

  18. E. Lukach, Characteristic Functions [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  19. P. D. T. A. Elliott, Probabilistic Number Theory II. Central Limit Theorems, Springer-Verlag, New York-Heidelberg-Berlin (1980).

    Google Scholar 

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V. Kapsukas Vilnius State University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 24, No. 3, pp. 148–161, July–September, 1984.

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Manstavičius, E. Arithmetic simulation of stochastic processes. Lith Math J 24, 276–285 (1984). https://doi.org/10.1007/BF00968047

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  • DOI: https://doi.org/10.1007/BF00968047

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