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Tytuł książki

Bilinear random integrals

Autorzy

Jan Rosiński

Seria

Rozprawy Matematyczne tom/nr w serii: 259 wydano: 1987

Zawartość

Pełne teksty:
rm25901.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
I. Introduction.....................................................................................................................................................................5
II. Preliminaries...................................................................................................................................................................7
  1. Infinitely divisible probability measures on Banach spaces..........................................................................................7
  2. Random measures......................................................................................................................................................9
III. Bilinear random integral...............................................................................................................................................11
  1. Definition and necessary conditions for the existence of a random integral...............................................................11
  2. Topology in the space of M-integrable functions........................................................................................................17
  3. Characterization of M-integrable functions.................................................................................................................21
  4. Approximation by simple functions and some contraction principles..........................................................................33
  5. Stable symmetric random integrals............................................................................................................................42
IV. Random integrals of Banach space valued functions with respect to real valued random measures..........................45
  1. Immediate corollaries from a general theory of random integrals and examples........................................................45
  2. Gaussian and stable random integrals......................................................................................................................51
  3. Comparison theorem and some applications.............................................................................................................62
References......................................................................................................................................................................70

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 259

Liczba stron

71

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCLIX

Daty

wydano
1987

Twórcy

autor
Jan Rosiński
  • Wrocław University, Institute of Mathematics, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • University of Tennessee, Mathematics Department, Knoxville, TN 37996, U.S.A.

Bibliografia

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  • [2] A. de Acosta, A. Araujo, E. Giné, Poisson measures, Gaussian measures and the central limit theorem in Banach spaces, in J. Kuelbs Ed, Advances in Probability, Vol. IV, 1-68, Dekker, New York 1978.
  • [3] A. Araujo, E. Giné, The central limit theorem for real and Banach valued random variables, Wiley, New York 1980.
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  • [16] Z. J. Jurek, W. Vervaat, An integral representation for selfdecomposable Banach space valued random variables, Z. Wahrsch. verw. Gebiete 62 (1983), 247-262.
  • [17] O. Kallenberg, Random measures, Academic Press, New York 1976.
  • [18] J. F. C. Kingman, Completely random measures, Pacific J. Math. 21, 1 (1967), 59-78.
  • [19] A. N. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, Doklady Akad. Nauk S5.S.R., 26 (1940), 115-118.
  • [20] A. N. Kolmogorov, La transformation de Laplace dans les espaces lineaires, Comptes Rendus Acad. Sci. Paris, 200 (1935), 1717-1718.
  • [21] W. Krakowiak, Operator semi-stable probability measures on Banach spaces. Coll. Math. 43 (1980). 351-363.
  • [22] W. Krakowiak, Semi-stable probability measures on Banach spaces, preprint.
  • [23] S. Kwapień, B. Szymański, Some remarks on Gaussian measures in Banach spaces. Probability Math. Statistics, 1.1 (1980), 59-65.
  • [24] J. T. Lapreste, Type et cotype et mesures de Lévy sur les espaces de Banach, Séminaire de l'Ecole Polytechnique, Exposé n° XXIII, 1977/1978.
  • [25] P. Lévy, Théorie de l'addition des variables aléatoires (Paris) 1937.
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  • [29] M. B. Marcus, W. A. Woyczyński, Stable measures and central limit theorems in spaces of stable type, Trans. Amer. Math. Soc. 251 (1979), 71-102.
  • [30] M. Metivier, J. Pellaumail, Notions de base sur l'intégrale stochastique. Séminaire de Probabilités de Rennes, 1976.
  • [31] M. Metivier, J. Pellaumail, Mesures stochastiques à valeurs dans des espaces $L_0$, Z. Wahr. (40) (1977), 101-114.
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  • [34] A. Prekopa, On stochastic set function. Acad.Scient.Hung. 7 (1956), 215-262, 8 (1957), 337-374, 8 (1957), 375-400.
  • [35] J. Rosiński, Random integrals of Banach space valued functions, Studia Math. 78 (1984), 15-38.
  • [36] J. Rosiński, On the convolution of cylindrical measures, Bull. Acad. Polon. Sci. Ser. Sci. Math. 30 (1982), 379-389.
  • [37] J. Rosiński, E. Rowecka, Random integrals and stable measures on Banach spaces, 1978, Preprint.
  • [38] J. Rosiński, Z. Suchanecki, On the space of vector-valued functions integrable with respect to the white noise, Coll. Math. 43, 1 (1980), 183-201.
  • [39] R. Sztencel, On boundedness and convergence of some Banach space valued random series, Probability Math. Statistics, 2, 1 (1981), 83-88.
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  • [48] M. Y or, Sur les integrates stochastiques a valeurs dans un espaces de Banach, Annales de l'Institut Henri Poincaré, Section B, 10 (1974), 31-36.
  • [49] V. V. Yurinski, On infinitely divisible distributions, Theory Probability and Its Appl. 192, (1974), 308-318.

Języki publikacji

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Identyfikator YADDA

bwmeta1.element.zamlynska-75305a1b-9ec4-4483-8a24-3cd1946045a1

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ISBN
83-01-07186-9
ISSN
0012-3862

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DML-PL
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