$\Lambda (q)$ processes
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- by Ron C. Blei PDF
- Trans. Amer. Math. Soc. 319 (1990), 777-786 Request permission
Abstract:
Motivated by some classical notions in harmonic analysis, $\Lambda (q)$ processes are introduced in the context of a study of stochastic interdependencies. An extension of a classical theorem of Salem and Zygmund regarding random Fourier series is obtained. The Littlewood exponent of $\Lambda (q)$ processes is estimated and, in some archetypical cases, computed.References
- Ron C. Blei, Multi-linear measure theory and multiple stochastic integration, Probab. Theory Related Fields 81 (1989), no. 4, 569–584. MR 995812, DOI 10.1007/BF00367304
- Ron Blei, Combinatorial dimension and certain norms in harmonic analysis, Amer. J. Math. 106 (1984), no. 4, 847–887. MR 749259, DOI 10.2307/2374326
- Ron C. Blei, $\alpha$-chaos, J. Funct. Anal. 81 (1988), no. 2, 279–297. MR 971881, DOI 10.1016/0022-1236(88)90101-2
- Ron C. Blei and J.-P. Kahane, A computation of the Littlewood exponent of stochastic processes, Math. Proc. Cambridge Philos. Soc. 103 (1988), no. 2, 367–370. MR 923689, DOI 10.1017/S030500410006494X
- Ron C. Blei, Measurements of interdependencies of stochastic increments, Commutative harmonic analysis (Canton, NY, 1987) Contemp. Math., vol. 91, Amer. Math. Soc., Providence, RI, 1989, pp. 29–36. MR 1002585, DOI 10.1090/conm/091/1002585
- J. Bourgain, Bounded orthogonal systems and the $\Lambda (p)$-set problem, Acta Math. 162 (1989), no. 3-4, 227–245. MR 989397, DOI 10.1007/BF02392838
- Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992 J. E. Littlewood, On bounded bilinear forms in an infinite number of variables, Quart. J. Math Oxford 1 (1930), 164-174.
- H. P. McKean, Geometry of differential space, Ann. Probability 1 (1973), 197–206. MR 353471, DOI 10.1214/aop/1176996973
- Walter Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227. MR 0116177, DOI 10.1512/iumj.1960.9.59013
- R. Salem and A. Zygmund, Some properties of trigonometric series whose terms have random signs, Acta Math. 91 (1954), 245–301. MR 65679, DOI 10.1007/BF02393433
- Norbert Wiener, The Homogeneous Chaos, Amer. J. Math. 60 (1938), no. 4, 897–936. MR 1507356, DOI 10.2307/2371268
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 319 (1990), 777-786
- MSC: Primary 60G05; Secondary 60G17
- DOI: https://doi.org/10.1090/S0002-9947-1990-0974517-3
- MathSciNet review: 974517