Strong approximation for set-indexed partial sum processes via KMT constructions III

Rio Emmanuel

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 319-338
  • ISSN: 1292-8100

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Emmanuel, Rio. "Strong approximation for set-indexed partial sum processes via KMT constructions III." ESAIM: Probability and Statistics 1 (1997): 319-338. <http://eudml.org/doc/104237>.

@article{Emmanuel1997,
author = {Emmanuel, Rio},
journal = {ESAIM: Probability and Statistics},
language = {eng},
pages = {319-338},
publisher = {EDP Sciences},
title = {Strong approximation for set-indexed partial sum processes via KMT constructions III},
url = {http://eudml.org/doc/104237},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Emmanuel, Rio
TI - Strong approximation for set-indexed partial sum processes via KMT constructions III
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 319
EP - 338
LA - eng
UR - http://eudml.org/doc/104237
ER -

References

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  2. BASS, R. F., ( 1985), Law of the iterated logarithm for partial-sum processes with finite variance. Z. Wahrsch. verw. Gebiete 70 591-608. Zbl0575.60034MR807339
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  5. BRETAGNOLLE, J. and MASSART, P., ( 1989), Hungarian constructions from the non-asymptotic viewpoint. Ann. Probab. 17 239-256. Zbl0667.60042MR972783
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  7. EINMAHL, U., ( 1987), Strong invariance principle for partial sums of independent random vectors. Ann. Probab. 15 1419-1440. Zbl0637.60041MR905340
  8. KOMLÓS, J., MAJOR, P. and TUSNÁDY, G., ( 1975), An approximation of partial sums of independent rv's and the sample df. I. Z. Wahrsch, verw, Gebiete 32 111-131. Zbl0308.60029MR375412
  9. KOMLÓS, J., MAJOR, P. and TUSNÁDY, G., ( 1976), An approximation of partial sums of independent rv's and the sample df. II. Z. Wahrsch. verw. Gebiete 34 35-58. Zbl0307.60045MR402883
  10. LAURENT-BONVALOT, F., ( 1991) Approximation forte de processus empiriques et applications. Thèse de doctorat, chapitre 2. Université Paris Sud. 
  11. PETROV, V. V., ( 1995), Limit theorems of probability theory: sequences of independent random variables. Oxford university press. Oxford. Zbl0826.60001MR1353441
  12. POLLARD, D. ( 1984), Convergence of stochastic processes. Springer Series in Statistics. Springer, Berlin. Zbl0544.60045MR762984
  13. RIO, E., ( 1990), Approximation forte pour des processus de sommes partielles indexés par les quadrants. Thèse de doctorat, chapitre 3. Université Paris Sud. 
  14. RIO, E., ( 1993a), Strong approximation for set-indexed partial sum Processes, via KMT constructions I. Ann. Probab. 21 759-790. Zbl0776.60045MR1217564
  15. RIO, E., ( 1993b), Strong approximation for set-indexed partial sum Processes, via KMT constructions II. Ann. Probab. 21 1706-1727. Zbl0779.60030MR1235436
  16. SAKHANENKO, A.I., ( 1985a), Rate of convergence in the invariance principle for non identically distributed variables with exponential moments. In Advances in probability theory. Limit theorems for sums of random variables (ed. A. A. Borovkov). 2-73. Optimization Software Inc., Publication Division. New York. Zbl0591.60027
  17. SAKHANENKO, A. I., ( 1985b), Estimates in the invariance principle. Trudy Inst. Mat. Sibirsk. Otdel, Akad. Nauka SSSR, Novosibirsk. 5 27-44. Zbl0585.60044MR821751
  18. SKOROHOD, A. V., ( 1976), On a representation of random variables. Theory Probab. Appl. 21 628-632. Zbl0362.60004MR428369
  19. TUSNÁDY, G., ( 1977), A remark on the approximation of the sample DF in the multidimensional case. Period. Math. Hung. 8 53-55. Zbl0386.60006MR443045

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