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Bulletin of the American Mathematical Society

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Book Review

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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. J. Bretagnolle, D. Dacunha-Castelle and J. L. Krivine, Lois stables et espaces L, Ann. Inst. Henri Poincaré 2 (1966), 231-259. MR 203757
  • 5. J. Bretagnolle and D. Dacunha-Castelle, Le determinisme des fonctions laplaciennes sur certains espaces de suites, Ann. Inst. Henri Poincaré 5 (1969), 1-12. MR 260008
  • 6. H. Cramer and M. R. Leadbetter, Stationary and related stochastic processes, Wiley, New York, 1967. MR 217860
  • 7. R. M. Dudley, The sizes of compact subsets of Hilbert space, and continuity of Gaussian processes, J. Funct. Anal. 1 (1967), 290-330. MR 220340
  • 8. P. Lévy, Processus stochastiques et mouvement brownien, Gauthier-Villars, Paris, 1948 (1st ed.), 1965 (2nd ed.). MR 190953
  • 9. H. P. McKean, Brownian motion with a several dimensional time, Theor. Probab. Appl. 8 (1963), 335-354. MR 157407
  • 10. L. D. Pitt, A Markov property of Gaussian processes with a multidimensional parameter, Arch. Rational Mech. Anal. 43 (1971), 367-391. MR 336798
  • 11. S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 24 (1945), 46-156. MR 11918
  • 12. I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. of Math. (2) 39 (1938), no. 4, 811–841. MR 1503439, https://doi.org/10.2307/1968466
  • 13. I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96--108. MR 5922
  • 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
American Mathematical Society