Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 1567236
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: I. A. Ibragimov and Yu. A. Rozanov
Title: Gaussian random processes
Additional book information: Applications of Math., volume 9, Springer-Verlag, New York-Heidelberg-Berlin, 1978, x + 276 pp., $24.80.

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

  • T. W. Anderson, An introduction to multivariate statistical analysis, Wiley Publications in Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0091588
  • R. Askey and N. H. Bingham, Gaussian processes on compact symmetric spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 37 (1976/77), no. 2, 127–143. MR 423000, DOI 10.1007/BF00536776
  • Albert Badrikian and Simone Chevet, Mesures cylindriques, espaces de Wiener et fonctions aléatoires Gaussiennes, Lecture Notes in Mathematics, Vol. 379, Springer-Verlag, Berlin-New York, 1974 (French). MR 0420760
  • Peter Baxendale, Gaussian measures on function spaces, Amer. J. Math. 98 (1976), no. 4, 891–952. MR 467809, DOI 10.2307/2374035
  • Ian F. Blake and William C. Lindsey, Level-crossing problems for random processes, IEEE Trans. Inform. Theory IT-19 (1973), 295–315. MR 370729, DOI 10.1109/tit.1973.1055016
  • Christer Borell, Gaussian Radon measures on locally convex spaces, Math. Scand. 38 (1976), no. 2, 265–284. MR 436303, DOI 10.7146/math.scand.a-11634
  • Herm Jan Brascamp and Elliott H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Functional Analysis 22 (1976), no. 4, 366–389. MR 0450480, DOI 10.1016/0022-1236(76)90004-5
  • John T. Cannon, Continuous sample paths in quantum field theory, Comm. Math. Phys. 35 (1974), 215–233. MR 351338
  • René Carmona, Measurable norms and some Banach space valued Gaussian processes, Duke Math. J. 44 (1977), no. 1, 109–127. MR 426119
  • René Carmona, Potentials on abstract Wiener space, J. Functional Analysis 26 (1977), no. 3, 215–231. MR 0466480, DOI 10.1016/0022-1236(77)90025-8
  • Simone Chevet, Un résultat sur les mesures gaussiennes, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 8, A441–A444. MR 428413
  • B. S. Cirel′son, I. A. Ibragimov, and V. N. Sudakov, Norms of Gaussian sample functions, Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975) Lecture Notes in Math., Vol. 550, Springer, Berlin, 1976, pp. 20–41. MR 0458556
  • R. M. Dudley, Sample functions of the Gaussian process, Ann. Probability 1 (1973), no. 1, 66–103. MR 346884, DOI 10.1214/aop/1176997026
  • H. Dym and H. P. McKean, Gaussian processes, function theory, and the inverse spectral problem, Probability and Mathematical Statistics, Vol. 31, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0448523
  • Constance M. Elson, An extension of Weyl’s lemma to infinite dimensions, Trans. Amer. Math. Soc. 194 (1974), 301–324. MR 343022, DOI 10.1090/S0002-9947-1974-0343022-0
  • Charles Fefferman, Max Jodeit Jr., and Michael D. Perlman, A spherical surface measure inequality for convex sets, Proc. Amer. Math. Soc. 33 (1972), 114–119. MR 293500, DOI 10.1090/S0002-9939-1972-0293500-1
  • J. Feldman, Correction to “Equivalence and perpendicularity of Gaussian processes”, Pacific J. Math. 9 (1959), 1295–1296. MR 108852
  • Jacob Feldman, Absolute continuity of stochastic processes, Lectures in Modern Analysis and Applications, III, Lecture Notes in Mathematics, Vol. 170, Springer, Berlin, 1970, pp. 71–86. MR 0272039
  • Xavier Fernique, Des résultats nouveaux sur les processus gaussiens, C. R. Acad. Sci. Paris Sér. A 278 (1974), 363–365 (French). MR 413237
  • X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, École d’Été de Probabilités de Saint-Flour, IV-1974, Lecture Notes in Math., Vol. 480, Springer, Berlin, 1975, pp. 1–96 (French). MR 0413238
  • James Glimm, The mathematics of quantum fields, Advances in Math. 16 (1975), 221–232. MR 368657, DOI 10.1016/0001-8708(75)90152-8
  • Leonard Gross, Abstract Wiener spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 31–42. MR 0212152
  • Leonard Gross, Potential theory on Hilbert space, J. Functional Analysis 1 (1967), 123–181. MR 0227747, DOI 10.1016/0022-1236(67)90030-4
  • Leonard Gross, Abstract Wiener measure and infinite dimensional potential theory, Lectures in Modern Analysis and Applications, II, Lecture Notes in Mathematics, Vol. 140, Springer, Berlin, 1970, pp. 84–116. MR 0265548
  • Leonard Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061–1083. MR 420249, DOI 10.2307/2373688
  • Alain Guichardet, Symmetric Hilbert spaces and related topics, Lecture Notes in Mathematics, Vol. 261, Springer-Verlag, Berlin-New York, 1972. Infinitely divisible positive definite functions. Continuous products and tensor products. Gaussian and Poissonian stochastic processes. MR 0493402
  • Sam Gutmann, Correlations of functions of normal variables, J. Multivariate Anal. 8 (1978), no. 4, 573–578. MR 520965, DOI 10.1016/0047-259X(78)90035-0
  • Jaroslav Hájek, A property of $J$-divergences of marginal probability distributions, Czechoslovak Math. J. 8(83) (1958), 460–463 (English, with Russian summary). MR 99712
  • Yaroslav Gaek, On a property of normal distribution of any stochastic process, Czechoslovak Math. J. 8(83) (1958), 610–618 (Russian, with English summary). MR 104290
  • Takeyuki Hida, Stationary stochastic processes, Mathematical Notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0258106
  • Takeyuki Hida, Analysis of Brownian functionals, Carleton Mathematical Lecture Notes, No. 13, Carleton University, Ottawa, Ont., 1975. MR 0451429
  • Takeyuki Hida, Generalized multiple Wiener integrals, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), no. 3, 55–58. MR 494538
    • 33.
    N. Jain, Notes on Gaussian processes, Univ. Minnesota School of Math., 1973, iii + 110 pp.
    34.
    N. L. Johnson and S. Kotz, Distributions in statistics: vol. 4, Continuous multivariate distributions, Wiley, New York, 1972.
  • Thomas Kailath, A view of three decades of linear filtering theory, IEEE Trans. Inform. Theory IT-20 (1974), 146–181. MR 465437, DOI 10.1109/tit.1974.1055174
  • Shizuo Kakutani, Determination of the spectrum of the flow of Brownian motion, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 319–323. MR 35924, DOI 10.1073/pnas.36.5.319
  • D. Kölzow, A survey of abstract Wiener spaces, Stochastic processes and related topics (Proc. Summer Res. Inst. Statist. Inference for Stochastic Processes, Indiana Univ., Bloomington, Ind., 1974, Vol. 1; dedicated to Jerzy Neyman), Academic Press, New York, 1975, pp. 293–315. MR 0378071
  • Hui Hsiung Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, Vol. 463, Springer-Verlag, Berlin-New York, 1975. MR 0461643
  • Ju. V. Linnik, A certain application of algebraic number theory to mathematical statistics, Trudy Mat. Inst. Steklov. 112 (1971), 22–29, 386 (Russian). Collection of articles dedicated to Academician Ivan Matveevič Vinogradov on his eightieth birthday, I. MR 0331586
  • Paul Malliavin, Un principe de transfert et son application au calcul des variations, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 3, A187–A189 (French, with English summary). MR 446048
    • 41.
    M. Marcus, Sample paths of Gaussian processes, Northwestern Univ., Dept. of Math., Lecture Note Series, no. 1, 1977.
  • H. P. McKean, Geometry of differential space, Ann. Probability 1 (1973), 197–206. MR 353471, DOI 10.1214/aop/1176996973
  • Kenneth S. Miller, Multidimensional Gaussian distributions, The SIAM Series in Applied Mathematics, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171333
  • Edward Nelson, Construction of quantum fields from Markoff fields, J. Functional Analysis 12 (1973), 97–112. MR 0343815, DOI 10.1016/0022-1236(73)90091-8
  • Edward Nelson, The free Markoff field, J. Functional Analysis 12 (1973), 211–227. MR 0343816, DOI 10.1016/0022-1236(73)90025-6
  • Jacques Neveu, Processus aléatoires gaussiens, Séminaire de Mathématiques Supérieures, No. 34 (Été, vol. 1968, Les Presses de l’Université de Montréal, Montreal, Que., 1968 (French). MR 0272042
  • M. Ann Piech, Smooth functions on Banach spaces, J. Math. Anal. Appl. 57 (1977), no. 1, 56–67. MR 458465, DOI 10.1016/0022-247X(77)90284-0
  • Ju. K. Beljaev (ed.), Sluchaĭ nye protsessy. Vyborochnye funtskii i peresecheniya, Matematika: Novoe v Zarubezhnoĭ Nauke [Mathematics: Recent Publications in Foreign Science], vol. 10, “Mir”, Moscow, 1978 (Russian). Translations by V. I. Piterbarg. MR 575867
  • Loren D. Pitt, A Gaussian correlation inequality for symmetric convex sets, Ann. Probability 5 (1977), no. 3, 470–474. MR 448705, DOI 10.1214/aop/1176995808
  • M. Reed and L. Rosen, Support properties of the free measure for Boson fields, Comm. Math. Phys. 36 (1974), 123–132. MR 351340
  • I. E. Segal, Tensor algebras over Hilbert spaces. I, Trans. Amer. Math. Soc. 81 (1956), 106–134. MR 76317, DOI 10.1090/S0002-9947-1956-0076317-8
  • I. E. Segal, Distributions in Hilbert space and canonical systems of operators, Trans. Amer. Math. Soc. 88 (1958), 12–41. MR 102759, DOI 10.1090/S0002-9947-1958-0102759-X
  • L. A. Shepp, Radon-Nikodým derivatives of Gaussian measures, Ann. Math. Statist. 37 (1966), 321–354. MR 190999, DOI 10.1214/aoms/1177699516
  • David Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463–501. MR 133183, DOI 10.1002/j.1538-7305.1962.tb02419.x
  • V. N. Sudakov, Geometric problems in the theory of infinite-dimensional probability distributions, Proc. Steklov Inst. Math. 2 (1979), i–v, 1–178. Cover to cover translation of Trudy Mat. Inst. Steklov 141 (1976). MR 530375
  • Norbert Wiener, The Homogeneous Chaos, Amer. J. Math. 60 (1938), no. 4, 897–936. MR 1507356, DOI 10.2307/2371268
  • Eugene Wong, Recent progress in stochastic processes—a survey, IEEE Trans. Inform. Theory IT-19 (1973), 262–275; correction, ibid. IT-19 (1973), 826. MR 371460, DOI 10.1109/tit.1973.1055102
    •
    Review Information:

    Reviewer: R. M. Dudley
    Journal: Bull. Amer. Math. Soc. 2 (1980), 373-378
    DOI: https://doi.org/10.1090/S0273-0979-1980-14768-0