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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF
Book Information:

Author: Erik Vanmarcke
Title: Random fields: analysis and synthesis
Additional book information: MIT Press, Cambridge, Mass., 1983, xii + 382 pp., $45.00. ISBN 0-262-22026-1.

Author: M. I. Yadrenko
Title: Spectral theory of random fields
Additional book information: Optimization Software, Inc., New York, N.Y., 1983, iii + 259 pp., $24.00. ISBN 0-911575-00-6.

References [Enhancements On Off] (What's this?)

  • 1. Robert J. Adler, The geometry of random fields, John Wiley & Sons, Ltd., Chichester, 1981. Wiley Series in Probability and Mathematical Statistics. MR 611857
  • 2. Simeon M. Berman, Isotropic Gaussian processes on the Hilbert sphere, Ann. Probab. 8 (1980), no. 6, 1093–1106. MR 602383
  • 3. Simeon M. Berman, Unboundedness of sample functions of stochastic processes with arbitrary parameter sets, with applications to linear and 𝑙_{𝑝}-valued parameters, Osaka J. Math. 21 (1984), no. 1, 133–147. MR 736975
  • 4. Jean Bretagnolle, Didier Dacunha-Castelle, and Jean-Louis Krivine, Lois stables et espaces 𝐿^{𝑝}, Ann. Inst. H. Poincaré Sect. B (N.S.) 2 (1965/1966), 231–259 (French). MR 0203757
  • 5. Jean Bretagnolle and Didier Dacunha-Castelle, Le déterminisme des fonctions laplaciennes sur certains espaces de suites, Ann. Inst. H. Poincaré Sect. B (N.S.) 5 (1969), 1–12 (French, with English summary). MR 0260008
  • 6. Harald Cramér and M. R. Leadbetter, Stationary and related stochastic processes. Sample function properties and their applications, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0217860
  • 7. R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis 1 (1967), 290–330. MR 0220340
  • 8. Paul Lévy, Processus stochastiques et mouvement brownien, Suivi d’une note de M. Loève. Deuxième édition revue et augmentée, Gauthier-Villars & Cie, Paris, 1965 (French). MR 0190953
  • 9. H. P. McKean Jr., Brownian motion with a several-dimensional time, Teor. Verojatnost. i Primenen. 8 (1963), 357–378. MR 0157407
  • 10. Loren D. Pitt, A Markov property for Gaussian processes with a multidimensional parameter, Arch. Rational Mech. Anal. 43 (1971), 367–391. MR 0336798
  • 11. S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 24 (1945), 46–156. MR 0011918
  • 12. I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. of Math. (2) 39 (1938), no. 4, 811–841. MR 1503439, 10.2307/1968466
  • 13. I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96–108. MR 0005922
  • 14. Michel Weber, Une méthode élémentaire pour l’étude de la régularité d’une large classe de fonctions aléatoires, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 12, 599–602 (French, with English summary). MR 615458

Review Information:

Reviewer: Simeon M. Berman
Journal: Bull. Amer. Math. Soc. 13 (1985), 57-62
DOI: https://doi.org/10.1090/S0273-0979-1985-15363-7