Some geometric properties of spaces associated with multiple stable integrals
HTML articles powered by AMS MathViewer
- by Jerzy Szulga PDF
- Proc. Amer. Math. Soc. 120 (1994), 457-464 Request permission
Abstract:
We investigate properties of vector lattices of multiply integrable functions with respect to a symmetric stable process.References
- Stamatis Cambanis, Jan Rosiński, and Wojbor A. Woyczyński, Convergence of quadratic forms in $p$-stable random variables and $\theta _p$-radonifying operators, Ann. Probab. 13 (1985), no. 3, 885–897. MR 799426 W. Feller, An introduction to probability theory and its applications, 2nd ed., Wiley, New York, 1971.
- J. L. Krivine, Théorèmes de factorisation dans les espaces réticulés, Séminaire Maurey-Schwartz 1973–1974: Espaces $L^{p}$, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. 22 et 23, Centre de Math., École Polytech., Paris, 1974, pp. 22 (French). MR 0440334
- Wiesław Krakowiak and Jerzy Szulga, Hypercontraction principle and random multilinear forms, Probab. Theory Related Fields 77 (1988), no. 3, 325–342. MR 931501, DOI 10.1007/BF00319292 —, Multilinear random forms, Ann. Probab. 14 (1988), 955-973.
- Wiesław Krakowiak and Jerzy Szulga, A multiple stochastic integral with respect to a strictly $p$-stable random measure, Ann. Probab. 16 (1988), no. 2, 764–777. MR 929077
- O. Kallenberg and J. Szulga, Multiple integration with respect to Poisson and Lévy processes, Probab. Theory Related Fields 83 (1989), no. 1-2, 101–134. MR 1012497, DOI 10.1007/BF00333146
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367
- Julian Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin, 1983. MR 724434, DOI 10.1007/BFb0072210
- Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
- J. Rosiński and W. A. Woyczyński, On Itô stochastic integration with respect to $p$-stable motion: inner clock, integrability of sample paths, double and multiple integrals, Ann. Probab. 14 (1986), no. 1, 271–286. MR 815970
- Jerzy Szulga, A note on hypercontractivity of stable random variables, Ann. Probab. 18 (1990), no. 4, 1746–1758. MR 1071822 —, Limit theorems of some randomized nonlinear functionals of empirical measures, Auburn University, preprint, 1991. —, Limit distributions of $U$-statistics resampled by symmetric stable laws, Probab. Theory Related Fields 94 (1990), 83-90.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 457-464
- MSC: Primary 60H05; Secondary 46E30, 46N30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1203992-3
- MathSciNet review: 1203992