대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권5호
  • /
  • Pages.1539-1554
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  • 2013
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE INVARIANCE PRINCIPLE FOR RANDOM SUMS OF A DOUBLE RANDOM SEQUENCE

  • Gao, Zhenlong (School of Mathematical Sciences Qufu Normal University) ;
  • Fang, Liang (College of Mathematic and Computer Sciences Changsha University of Science and Technology, College of Mathematic and Computer Sciences Hunan Normal University)
  • 투고 : 2012.06.02
  • 발행 : 2013.09.30
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초록

In this paper, we extend Donsker's invariance principle to the case of random partial sums processes based on a double sequence of row-wise i.i.d. random variables.

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참고문헌

  1. P. Billingsley, Convergence of Probability Measures, John Wiley & Sons, New York, 1968.
  2. A. D'Aristotile, An invariance principle for triangular arrays, J. Theoret. Probab. 13 (2000), no. 2, 327-341. https://doi.org/10.1023/A:1007801726073
  3. A. de Acosta, Invariance principle in probability for triangular arrays of B-valued ran- dom vectors and some applications, Ann. Probab. 10 (1982), no. 2, 346-373. https://doi.org/10.1214/aop/1176993862
  4. M. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc. (1951). no. 6, 1-12.
  5. P. Erdos and M. Kac, On certain limit theorems of the theory of probability, Bull. Amer. Math. Soc. 52 (1946), no. 2, 292-302. https://doi.org/10.1090/S0002-9904-1946-08560-2
  6. P. Erdos and M. Kac, On the number of positive sums of independent random variables, Bull. Amer. Math. Soc. 53 (1947), no. 10, 1011-1020. https://doi.org/10.1090/S0002-9904-1947-08928-X
  7. D. H. Fearn, Galton-Watson processes with generation dependence, Proceedings of the Sixth Berkeley Symposium onMathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. IV: Biology and health, pp. 159-172. Univ. California Press, Berkeley, Calif., 1972.
  8. P. Hall and C. C. Heyde, Martingale Limit Theory and Its Application, Academic Press, New York, 1980.
  9. T. H. Hu, The invariance principle and its applications to branching processes, Acta Sci. Natur. Univ. Pekinensis 10 (1964), 1-27.
  10. K. S. Kubacki and D. Szynal, On the limit behaviur of random sums of independent random variables, Probab. Math. Statist. 5 (1985), no. 2, 235-249.
  11. M. Peligrad, Invariance principle for mixing sequences of random variables, Ann. Probab. 10 (1982), no. 4, 968-981. https://doi.org/10.1214/aop/1176993718
  12. A. Rackauskas and C. Suquet, Holderian invariance principle for triangular arrays of random variables, Lith. Math. J. 43 (2003), no. 4, 423-438. https://doi.org/10.1023/B:LIMA.0000009690.57986.d1
  13. Q. M. Shao, On the invariance principle for stationary-mixing sequences of random variables, Chinese Ann. Math. 10B (1989), 427-433.