About Georgian Academy of Sciences

Members

Georgian Academy of Sciences

Nicholas N. Vakhania

Full member of the Georgian Academy of Sciences

Birth information August 28, 1930, Kutaisi, Georgia

Graduate study Moscow State University, Department of Mathematics

Degrees Kandidat of Phys. Math. Sc., 1958, Moscow State University; Doktor of Phys. Math. Sc., 1969, Tbilisi State University

Main areas of research Probability Theory, Functional Analysis, Probability Measures on

Infinite Dimensional Linear Spaces

Position (principal) Institute of Computational Mathematics of the Georgian Academy of Sciences

(Tbilisi, Georgia) from 1957; from 1961 Head of the Department of

Probability Theory and Functional Analysis; from 1979 Director of the

institute

Position (secondary) Tbilisi State University, 1970 - 1973 Chairman of the Department of Cybernetics and Applied Mathematics; from 1970 Professor and Head of the Chair of Stochastic Processes

Visiting positions

Fulbright scholar at the University of Tennessee, Knoxville, Tenn., three months in spring of 1975
Fulbright scholar at the University of Minnesota, Minneapolis, Minn., three months in fall of 1975
Visiting professor at the University of California, Santa Barbara, Calif., two months in winter of 1976
Fulbright scholar at the Wayne State University, Detroit, Mich., three months in spring of 1980
Visiting professor at the University of North Carolina, Chapel Hill N. C., two months in spring of 1989
Visiting professor at CIMAT, Guanajuato, Mexico, six months in 1993-1994
Short time visiting positions at different universities of Australia, France, Germany, Greece, India, Italy, Japan, Mexico, Poland, Spain, United Kingdom, USA

Career-related activities

Member of the editorial Board of "Encyclopedia of Probability Theory and Mathematical Statistics", Moscow (editor of the section "Probability on Infinite-dimensional Spaces");
Member of the editorial Board of "Georgian Encyclopedia" (editor of the section of mathematics);
Member of the editorial board of "Probability Theory and it's Applications", Moscow
Member of the editorial board of "Georgian Mathematical Journal";
Member of the editorial board of "Bulletin of the Georgian Academy of Sciences" (Deputy Editor-in Chief)
Chairman of the Committee on Scientific Degrees in Probability Theory and Mathematical statistics, and Computational Mathematics at Georgian Academy of Sciences;

Awards, Honors Razmadze prize in Mathematics of the Georgian Academy of Sciences,

N.Muskhelishvili prize in Mathematics of the Georgian Academy of Sciences

Honored Scientist of Georgia

Fellow of World Innovation Foundation

Professional membership

Georgian Mathematical Union;
Statistical Association of Georgia;
American Mathematical Society;
International Statistical Institute

Publications

Books:

Probability Distributions in Linear Spaces. North Holland, 1980 (translated from Russian)
Probability Distributions on Banach Spaces. D. Reidel (Kluwer), 1987 (with S. Chobanyan and V. Tarieladze. Translated from Russian)

Main research papers:

On boundary value problem with the data on the whole boundary for a hyperbolic system equivalent to the vibrating string equation. Dokl. Akad. Nauk, 116 (1957), No. 6, 906-909
On stability of angular velocity of the rotation of a top full of liquid. Prikl. Mat. Mekh., 29 (1965), No. 1, 35-45
Sur une propriete des reparticions normales de probabilites dans les espaces $l_p$ et $H$. C. R. Acad. Sci. Paris Ser. 1 Math., 260 (1965), 1334-1336
Sur les reparticions de probabilites dans les espaces de suites numeriques. C. R.. Acad. Sci. Ser. 1 Math., 260 (1965), 1560-1562
On non-degenerate probability distributions in the spaces $l_p$. Teor. Veroyatnost. i primenen, 11 (1966), No. 3, 524-528
On a probability problem for the one-dimensional heat equation. Teor. Veroyatnost.i Primenen., 12 (1967), No. 4, 727-729
A note on the intersection of a sequence of embedded sets. Mat. Zametki , 3 (1968), No. 2, 165-170 (with I. Kartsivadze)
On an existence condition for Pettis integral. Studia Math., 29 (1968), No. 3, 243-248)
Covariance operator of probability distributions in Banach spaces. Bull. Georgian Acad. Sci., 51 (1968), No. 1, 35-40
On the covariance of random elements in linear spaces. Bull. Georgian Acad. Sci., 53 (1969), No. 1, 17-20
On a property of Gaussian distributions on Banach spaces. Sankhya, Ser A, p. 1, 35 (1973), 23-28
Trдger des Gausshen masses in Hilbertraum. Math. Nachr., 64 (1974), 319-322
The toplogical support of Gaussian measures in Banach spaces. Nagoya Math. J., 57 (1975), 59-63
Prolongment d'une dualite $(X,Y)$ entre espaces vectoriels en une dualite de type $(L_q, L_p)$. C. R. Acad. Sci. Paris Ser. 1 Math., 284 (1977), 1561-1564 (with V. Tarieladze and A. Tortrat)
On the support of Gaussian probability measures on locally convex spaces. In: Multivariate Analysis 4, P. R. Krishnayah ed., 1977, 297-309 (with B. Rajput)
Covariance operator of probability measures on locally convex spaces. Theory Probab. Appl., 23 (1978), No. 1, 1-21 (with V. Tarieladze)
On the relation between the concepts of Gaussian measures and Gaussian processes. Mat. Zametki, 25 (1979), No. 7, 293-297
On continuity of random linear functionals. Teor. Veroyatnost. i primenen., 26 (1981), No. 1, 172-178 (with V. Tarieladze and A. Tortrat)
On Lord's paradox of mean absolute deviation. Dokl. Akad. Nauk, 287 (1986), No. 2, 265-268
On the problem of best approximation in a space of vector-valued functions. Dokl. Akad. Nauk, 25 (1982), No. 3, 565-568 (with S. Chobanyan)
The linear prediction and approximation of weak second order random elements. In: Prediction Theory and Harmonic Analysis, V. Mandrekar and H. Salehi eds. North Holland, 1983, 37-60 (with S. Chobanyan)
On orthogonal random vectors in Hilbert space. Dokl. Akad. Nauk 294 (1987), No. 3, 528-531 (with N. Kandelaki)
A generalization of the Hurwitz-Radon-Eckman theorem and orthogonal random vectors. Dokl. Akad. Nauk, 296 (1987), No. 2, 265-266 (with N. Kandelaki)
A. N. Kolmogorov and the developement of the Theory of Probability distributions on linear spaces. Teor.Veroyatnost. i Primenen, 34 (1989), No. 1, 197-202
Gaussian mean boundedness of densely defined linear operators. J. Complexity, 7 (1991), 225-231
Elementary proofs of Polya's characterization theorem and of the necessity of second moment in CLT. Theory Probab. Appl., 38 (1993), No. 1, 166-168
Canonical factorization of Gaussian covariance operators and some of its applications. Theory Probab. Appl., 38 (1993), No. 3, 498-505
On boundary value problems for the hyperbolic case. J. Complexity, 10 (1994), 341-355
Orthogonal random vectors in Hilbert space and a related problem of linear algebra. In: Notas de Investigacion 11, Proc. of III-d Mexican Simposium on Probab. Theory and Stochast. Proces., Mexican Mathematical Society, M. E. Caballero and L. G. Gorostiza eds., 1994, 13- 30
Random vectors with values in complex Hilbert spaces. Theory Probab. Appl., 41 (1996), No. 1, 116-131 (with N. Kandelaki)
On singularity and equivalence of Gaussian measures. In: Real and Stochastic Analysis, Recent Advances, M. M. Rao ed., 1997, 367-387 (with V. Tarieladze)
Polya's characterization theorem for complex random variables. J. Complexity, 13 (1997), 480-488
Random vectors with values in quaternion Hilbert spaces. Theory Probab. Appl., 43 (1998), No. 1, 99-115
Absolute and unconditional convergence in $l_1$. Bull. Georgian Acad. Sci., 160 (1999), No. 2, 201-203 (with V. Kvaratskhelia)
On a criterion for unconditional convergence of Hadamard series in the spaces l_p, Bull. Georgian Acad. Sci., 162 (2000), No. 2, 199-202 (with V. Kvaratskhelia)
On subgaussian random vectors in normed spaces. Bull. Georgian Acad. Sci., 163 (2001), No. 1. 8-11
On orthogonal multiplication in complex Hilbert spaces. Theor. Probability and Math. Statist., No. 63, 2001, 27-32 (with N.Kandelaki)
On the concept of complex Gaussin random vectors. Ukrainian Mahtematical Congress - 2001. Probability Theory and Mathematical Statistics. Section 9. Proceedings Institute of Mathematics, Kyiv, 2002, 170-177
An application of the Brunel-Sucheston spreading model. Bull. Georgian Acad. Sci.,165(2002), No.3, 455-457 (with V.Kvaratskhelia)

Expository papers in:

Mathematical Encyclopedia, 5, “Sovetskaya Enciklopedia”, Moscow, 1985
Encyclopedia of Probability theory and Mathematical Statistics, “Bolshaya Rossiiskaia Enciklopedia”, Moscow, 1999
"Georgian Encyclopedia" (editor of the section of mathematics)

Main invited talks at:

Recent Trends in Statistics, Calcutta, India, December 16-29, 1974;
Fifth International Symposium on Multivariate Analysis, Pittsburgh, USA, June 19-24, 1978;
Fifth International Symposium on Information Theory, Tbilisi, Georgia, July 3-7, 1979;
Eighth International Conference on Mathematical Statistics and Probability, Wisla, Poland, December 4-10, 1980;
Fourteenth European Meeting of Statisticians, Wroclaw, Poland, August 31-September 4, 1981;
First World Congress of Bernoulli Society, Tashkent, Uzbekistan, September 8-14, 1986;
Third Symposium on Probability and Stochastic Processes of the Mexican Mathematical Society, Hermosillo, Mexico, March 7-11, 1994;
Dagsthul Seminars on Algorithms and Complexity, Saarbrucken, Germany, April 15-19, 1991, October 12-16, 1992, October 21-25, 1996;
Special semesters at Stefan Banach International Mathematical Center in Warsaw, Poland, in Geometry of Banach Spaces and its Applications, February-March, 1982, Probability Theory and Mathematical Statistics, April 17 - May 15, 1989, Approximation and Complexity, February 6-24, 1995;
Vilnius International Conferences on Probability Theory and Mathematical Statistics I-V
The International conference "Stochastic Analysis and it's applications", June 10-17, 2001, Lviv, Ukraine.

Mailing address

Prof. N. Vakhania, Director,
Institute of Computational Mathematics,
Georgian Academy of Sciences,
Akuri str. 8, Tbilisi 93, Georgia

Tel: +995 32 33 24 38 (office), +995 32 38 36 23 (home)
Fax: +995 32 99 88 23
E-mail: [email protected]

Send all comments to: [email protected]