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Limit theorems for random fields

Seria
Rozprawy Matematyczne tom/nr w serii: 186 wydano: 1981
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CONTENTS
Introduction............................................................................................................................................................................ 5
1. Notation and preliminaries............................................................................................................................................ 5
2. Statement of the problem............................................................................................................................................... 9
3. Norming sequences....................................................................................................................................................... 11
4. A characterization of full measures belonging to $N_d(X)$.................................................................................... 16
5. A characterization of multiply ${T_t}$-decomposable probability measures on X............................................. 22
6. A reduction of the problem............................................................................................................................................. 27
7. Multiply monotone functions.......................................................................................................................................... 29
8. The Urbanik representation for d-times ${T_t}$-decomposable (d = 1,2,...) probability measures on X...... 31
9. The Urbanik representation for completely ${T_t}$-decomposable probability measures on X..................... 34
References............................................................................................................................................................................ 39
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 186
Liczba stron
39
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXXVI
Daty
wydano
1981
Twórcy
Bibliografia
  • [1] G. Choquet, Le théorème de représentation intégrale dans les ensemble convexes compact, Ann. Inst. Fourier 10 (1960), pp. 333-344.
  • [2] E. Dettweiler, Grenzwertsätze für Wahrscheinlichkeitsmasse auf Badrikianschen Räumen, Thesis_Eberhard-Karls Universität zu Tübingen, 1974.
  • [3] K. Ito and M. Nisio, On the convergence of sums of independent Banach space valued random variables, Osaka J. of Math. 5 (1968), pp. 35-48.
  • [4] N. S. Jain and G. Kallianpur, Norm convergent expansions for Gaussian processes in Banach spaces, Proc. Amer. Math. Soc. 25 (1970), pp. 890-895.
  • [5] A. Kumar and B. M. Schreiber, Self-decomposable probability measures on Banach spaces, Studia Math. 53 (1975), pp. 55-71.
  • [6] P. Lévy, Théorie de raddition des variables aléatoires, Paris 1954.
  • [7] M. Loéve, Probability Theory, New York 1950.
  • [8] Nguyen Van Thu, Multiply self-decomposable probability measures on Banach spaces, Studia Math. 66 (1980), pp. 161-175.
  • [9] Nguyen Van Thu, Banach space valued Brownian motions I, Acta Math. Vietnam 3 (1978), pp. 35-40.
  • [10] Nguyen Van Thu, Banach space valued Brownian motions II: A stochastic integral of operator-valued functions, ibid. 3 (1978), 44-46.
  • [11] A. B. Paalman-de Miranda, Topological Semigroup, Amsterdam 1964.
  • [12] K. R. Parthasarathy, Probability Measures on Metric Spaces, New York-London 1967,
  • [13] M. Sharpe, Operator-stable probability distributions on vector groups, Trans. Amer. Math. Soc. 136 (1969), pp. 51-65.
  • [14] A. Tortrat, Structure des lois Indéfiniment divisibles dans un espace vectorial topologique (séparé) X, Symposium on Probability Methods in Analysis, Lecture Notes in Mathematics 31, Berlin-Heidelberg-New York 1967, pp. 299-328.
  • [15] A. Tortrat, Sur la structure des lois indéfiniment divisibles dans les espaces vectoriels, Z. Wahrscheinlichkeitstheorie verw. Geb. 11 (1969), pp. 311-326.
  • [16] K. Urbanik, Levy's probability measures on Euclidean spaces, Studia Math, 44 (1972), pp. 119-148.
  • [17] K. Urbanik, Levy's probability measures on Banach spaces, ibid. 63 (1978), pp. 284-308.
  • [18] N. N. Vahaniya, Probability distributions on linear spaces (in Russian), Tbilisi 1971.
  • [19] R. E. Williamson, Multiply monotone functions and their Laplace transforms, Duke Math. J. 23 (1956), pp. 189-207.
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Identyfikator YADDA
bwmeta1.element.zamlynska-31e87fdb-0673-44e5-85d3-739c9b7c57ec
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ISBN
83-01-01122-X
ISSN
0012-3862
Kolekcja
DML-PL
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