Limit theorems for B -lattice valued random variables

Marta Urbaníková

Mathematica Slovaca (2002)

  • Volume: 52, Issue: 1, page 99-108
  • ISSN: 0232-0525

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Urbaníková, Marta. "Limit theorems for $B$-lattice valued random variables." Mathematica Slovaca 52.1 (2002): 99-108. <http://eudml.org/doc/32218>.

@article{Urbaníková2002,
author = {Urbaníková, Marta},
journal = {Mathematica Slovaca},
keywords = {Banach lattice random variables; stochastically dominated random variables},
language = {eng},
number = {1},
pages = {99-108},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Limit theorems for $B$-lattice valued random variables},
url = {http://eudml.org/doc/32218},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Urbaníková, Marta
TI - Limit theorems for $B$-lattice valued random variables
JO - Mathematica Slovaca
PY - 2002
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 52
IS - 1
SP - 99
EP - 108
LA - eng
KW - Banach lattice random variables; stochastically dominated random variables
UR - http://eudml.org/doc/32218
ER -

References

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  1. CHOW Y. S., LAI T. L., Limiting behavior of weighted sums of independent random variables, Ann. Probab. 1 (1973), 810-824. (1973) Zbl0303.60025MR0353426
  2. CRISTESCU R., Sur la représentation intégrale de certains opérateurs linéeires, Rev. Roumaine Math. Pures Appl. 25 (1980), 519-524. (1980) MR0577044
  3. KANTOROVITCH V. L., VULICH B. Z., PINSKER A. G., Funkcional'nyj analiz v poluuporiadochennych prostranstvakh, Gos. izd. techn. lit., Moskva, 1950. (Russian) (1950) 
  4. KELEMENOVÁ M., On the expected value of vector lattice-valued random variables, Acta Math. Univ. Comenian. 56-57 (1988), 153-157. (1988) MR1083018
  5. LOEVE M., Probability Theory, (3rd ed.), Van Nostrand, London, 1963. (1963) Zbl0108.14202MR0203748
  6. PADGETT W. J., TAYLOR R. L., Almost sure convergence of weighted sums of random elements in Banach spaces, In: Probability in Banach Spaces, Oberwolfach, 1975. Lecture Notes in Math. 526, Springer, Berlin, 1976, pp. 187-202. (1975) MR0455065
  7. POTOCKÝ R., A weak law of large numbers for vector lattice-valued random variables, Acta Math. Univ. Comenian. 42-43 (1983), 211-214. (1983) Zbl0538.60012MR0740751
  8. POTOCKÝ R., A strong law of large numbers for identically distributed vector lattice-valued random variables, Math. Slovaca 34 (1984), 67-72. (1984) Zbl0599.60038MR0735937
  9. POTOCKÝ R., On the expected value of vector lattice-valued random variables, Math. Slovaca 36 (1986), 401-405. (1986) Zbl0621.60002MR0871780
  10. SCHAEFER H. H., Banach Lattices and Positive Operators, Grundlehren Math. Wiss. 215, Springer-Verlag, Berlin-Heidelberg-New York, 1974. (1974) Zbl0296.47023MR0423039
  11. SZULGA J., Lattice moments of random vectors, Bull. Polish Acad. Sci. Math. 28 (1980), 87-93. (1980) Zbl0486.60007MR0616206
  12. TAYLOR R. L., Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces, Lecture Notes in Math. 672, Springer, Berlin, 1978. (1978) Zbl0443.60004MR0513422
  13. WANG X. C., BHASKARA RAO M., A note on convergence of weighted sums of random variables, J. Multivariate Anal. 15, 124-134. Zbl0583.60021MR0755820

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