Bulletin of the American Mathematical Society

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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.

Robert J. Adler, The geometry of random fields, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Ltd., Chichester, 1981. MR 611857

Simeon M. Berman, Isotropic Gaussian processes on the Hilbert sphere, Ann. Probab. 8 (1980), no. 6, 1093–1106. MR 602383

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

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

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

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

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, DOI 10.1016/0022-1236(67)90017-1

Paul Lévy, Processus stochastiques et mouvement brownien, Gauthier-Villars & Cie, Paris, 1965 (French). Suivi d’une note de M. Loève; Deuxième édition revue et augmentée. MR 0190953

H. P. McKean Jr., Brownian motion with a several-dimensional time, Teor. Verojatnost. i Primenen. 8 (1963), 357–378. MR 0157407

Loren D. Pitt, A Markov property for Gaussian processes with a multidimensional parameter, Arch. Rational Mech. Anal. 43 (1971), 367–391. MR 336798, DOI 10.1007/BF00252003

S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 24 (1945), 46–156. MR 11918, DOI 10.1002/j.1538-7305.1945.tb00453.x

I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. of Math. (2) 39 (1938), no. 4, 811–841. MR 1503439, DOI 10.2307/1968466

I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96–108. MR 5922

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

1.

R. J. Adler, The geometry of random fields, Wiley, Chichester, 1981. MR 0611857

2.

S. M. Berman, Isotropic Gaussian processes on the Hilbert sphere, Ann. Probab. 8 (1980), 1093-1106. MR 602383

3.

S. M. Berman, Unboundedness of sample functions of stochastic processes with arbitrary parameter sets, with applications to linear and l, Osaka J. Math. 21 (1984), 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), 811-841. MR 1503439

13.

I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96--108. MR 5922

14.

M. Weber, Une méthode élémentaire pour l'étude de la régularité d'un large classe de fonctions aléatoires, C. R. Acad. Sci. Paris Ser. A 292 (1981), 599-602. MR 615458