Strong laws of large numbers in certain linear spaces

Wojbor A. Woyczynski

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 2, page 205-223
  • ISSN: 0373-0956

Abstract

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In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous F -norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.

How to cite

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Woyczynski, Wojbor A.. "Strong laws of large numbers in certain linear spaces." Annales de l'institut Fourier 24.2 (1974): 205-223. <http://eudml.org/doc/74174>.

@article{Woyczynski1974,
abstract = {In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous $F$-norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.},
author = {Woyczynski, Wojbor A.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {205-223},
publisher = {Association des Annales de l'Institut Fourier},
title = {Strong laws of large numbers in certain linear spaces},
url = {http://eudml.org/doc/74174},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Woyczynski, Wojbor A.
TI - Strong laws of large numbers in certain linear spaces
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 2
SP - 205
EP - 223
AB - In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous $F$-norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.
LA - eng
UR - http://eudml.org/doc/74174
ER -

References

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  1. [1] A. BECK, A convexity condition in Banach spaces and the strog law of large numbers, Proc. Amer. Math. Soc., 13 (1962), 329-334. Zbl0108.31401MR24 #A3681
  2. [2] A. BECK and D. P. GIESY, P-uniform convergence and a vector-valued strong laws of large numbers, Trans. Amer. Math. Soc., 147 (1970), 541-559. Zbl0198.51006MR41 #7728
  3. [3] N. DUNFORD and J. T. SCHWARTZ, Linear operators, Vol. I, Wiley-Interscience, New York, 1958. Zbl0084.10402MR22 #8302
  4. [4] R. FORTET and E. MOURIER, Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math., 15 (1955), 62-79. Zbl0068.11104MR19,1202b
  5. [5] J. HOFFMANN-JORGENSEN, Sums of independent Banach space valued random variables, Aarhus Universitet, Matematisk Institut, Preprint Series, 1972/1973, No 15, 1-89. 
  6. [6] J.-P. KAHANE, Some random series of functions, Heath, Lexington, 1968. Zbl0192.53801MR40 #8095
  7. [7] V. V. PETROV, Sums of independent random variables, Nauka, Moscow, 1972 (in Russian). Zbl0288.60050MR46 #4606
  8. [8] V. V. PETROV, On the rate of growth of dependent random variables, Teor. Probability Appl., 18 (1973), 358-361. Zbl0295.60020MR47 #7792
  9. [9] P. RÉVÉSZ, The laws of large numbers, Academic Press, New York, 1968. Zbl0203.50403MR39 #6391
  10. [10] S. ROLEWICZ, Metric linear spaces, PWN, Warsaw, 1972. Zbl0226.46001MR55 #10993
  11. [11] W. A. WOYCZYŃSKI, Random series and laws of large numbers in some Banach spaces, Theor. Probability Appl., 18 (1973), 361-367. Zbl0324.60041MR47 #7793

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