Lithuanian Mathematical Journal

, Volume 19, Issue 3, pp 309–317 | Cite as

Limit theorems for time of first passage across a step bound

  • Sh. A. Mirakhmedov


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    Yu. V. Prokhorov, “Convergence of stochastic processes and limit theorems in probability theory,” Teor. Veroyatn. Ee Primen.,1, No. 2, 177–238 (1956).Google Scholar
  2. 2.
    A. V. Skorokhod, Studies in Stochastic Processes [in Russian], Kiev State Univ., Kiev (1961).Google Scholar
  3. 3.
    S. V. Nagaev, “On the rate of convergence in a boundary problem. I,” Teor. Veroyatn. Ee Primen.,15, No. 2, 179–199 (1970).Google Scholar
  4. 4.
    A. A. Borovkov, “On the rate of convergence in the invariance principle,” Teor. Veroyatn. Ee Primen.,18, No. 2, 218–233 (1973).Google Scholar
  5. 5.
    A. I. Sokhanenko, “On the rate of convergence in a boundary problem,” Teor. Veroyatn. Ee Primen.,19, No. 2, 416–421 (1974).Google Scholar
  6. 6.
    I. I. Migai and V. B. Nevzorov, “Limit theorems for the time of first attainment of a level,” Teor. Veroyatn. Ee Primen.,21, No. 2, 417–420 (1976).Google Scholar
  7. 7.
    Sh. A. Mirakhmedov, “The asymptotic distribution of the time of first passage of a random walk past a step boundary,” in: Proceedings of the Second Vilnius Conference: Prob. Theory Math. Stat. [in Russian], Vol. 2, Vilnius (1977).Google Scholar
  8. 8.
    Sh. A. Mirakhmedov, “On estimates of the rate of convergence in limit theorems for first passage time of a random walk,” Mat. Zametki,23, No. 3, 487–495 (1978).Google Scholar
  9. 9.
    W. Rosenkrantz, “On rates of convergence results for the invariance principle,” Trans. Am. Math. Soc.,129, 542–552 (1967).Google Scholar
  10. 10.
    J. Komlos, R. Major, and G. Tusnady, “Weak convergence and embedding,” in: Colloq. Mathematica Soc. Janos Bolyai, Limit Theorems of Probability Theory, Vol. 11, Koszthely (Hungary) (1974).Google Scholar
  11. 11.
    S. Sawyer, “Uniform limit theorems for the maximum comulative sum in probability,” Trans. Am. Math. Soc.,32, 363–367 (1968).Google Scholar
  12. 12.
    P. Erdös and M. Kac, “On certain limit theorems of the theory of probability,” Bull. Am. Math. Soc.,52, 292–302 (1946).Google Scholar
  13. 13.
    V. B. Nevzorov, Candidate's Dissertation, Leningrad (1972).Google Scholar
  14. 14.
    C. C. Heyde, “On extended rate of convergence results for the invariance principle,” Ann. Math. Stat.,40, No. 6, 2178–2179 (1969).Google Scholar
  15. 15.
    Sh. A. Mirakhmedov and A. N. Startsev, “On limit distributions in problems with a step boundary,” Izv. Akad. Nauk Uzbek SSR, Ser. Fiz.-Mat. Nauk, No. 3, 30–37 (1975).Google Scholar
  16. 16.
    A. N. Startsev, “Some results related to the invariance principle,” in: Probability Processes and Mathematical Statistics [in Russian], FAN, Uzbek SSR (1978), pp. 146–151.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Sh. A. Mirakhmedov

There are no affiliations available

Personalised recommendations