Ildar Abdullovich Ibragimov (on his ninetieth birthday)

A. A. Borovkov   ; Al. V. Bulinski   ; A. M. Vershik   ; D. Zaporozhets   ; A. S. Holevo   ; A. N. Shiryaev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 3, pp. 573-583

Bibliographie

[1] G. Baxter, “A convergence equivalence related to polynomials orthogonal on the unit circle”, Trans. Amer. Math. Soc., 99 (1961), 471–487 | DOI | MR | Zbl

[2] S. N. Bernstein, “One property characterizing Gauss's law”, Tr. Leningrad. Politekhn. Inst., 3 (1941), 21–22 (Russian)

[3] P. Billingsley, “The Lindeberg–Lévy theorem for martingales”, Proc. Amer. Math. Soc., 12:5 (1961), 788–792 | DOI | MR | Zbl

[4] A. Bloch and G. Pólya, “On the roots of certain algebraic equations”, Proc. London Math. Soc. (2), 33 (1931), 102–114 | DOI | MR | Zbl

[5] A. N. Borodin and I. A. Ibragimov, “Limit theorems for functionals of random walks”, Proc. Steklov Inst. Math., 195 (1995), 1–259 | MR | Zbl

[6] G. A. Brosamler, “An almost everywhere central limit theorem”, Math. Proc. Cambridge Philos. Soc., 104:3 (1988), 561–574 | DOI | MR | Zbl

[7] N. N. Čencov (Chentsov), “Estimation of an unknown distribution density from observations”, Soviet Math. Dokl., 3 (1963), 1559–1562 | MR | Zbl

[8] N. N. Čencov (Chentsov), Statistical decision rules and optimal inference, Transl. Math. Monogr., 53, Amer. Math. Soc., Providence, RI, 1982, viii+499 pp. | MR | Zbl

[9] Pao-Liu Chow, I. A. Ibragimov, and R. Z. Khasminskii, “Statistical approach to some ill-posed problems for linear partial differential equations”, Probab. Theory Related Fields, 113:3 (1999), 421–441 | DOI | MR | Zbl

[10] G. Darmois, “Analyse générale des liaisons stochastiques. Étude particulière de l'analyse factorielle linéaire”, Rev. Inst. Internat. Statist., 21 (1953), 2–8 | DOI | MR | Zbl

[11] P. Erdős and A. C. Offord, “On the number of real roots of a random algebraic equation”, Proc. London Math. Soc. (3), 6 (1956), 139–160 | DOI | MR | Zbl

[12] S. G. Ghurye and I. Olkin, “A characterization of the multivariate normal distribution”, Ann. Math. Statist., 33:2 (1962), 533–541 | DOI | MR | Zbl

[13] R. Z. Hasminskii (Khas'minskii) and I. A. Ibragimov, “On a lower bound for moments of point estimators”, Ann. Statist., 3 (1975), 228–233 | DOI | MR | Zbl

[14] I. A. Ibragimov, “On the composition of unimodal distributions”, Theory Probab. Appl., 1:2 (1956), 255–260 | DOI | MR | Zbl

[15] I. A. Ibragimov, “On estimation of the spectrum of a stationary Gaussian process”, Soviet Math. Dokl., 2 (1962), 1441–1444 | MR | Zbl

[16] I. A. Ibragimov, “Some limit theorems for stationary processes”, Theory Probab. Appl., 7:4 (1962), 349–382 | DOI | MR | Zbl

[17] I. A. Ibragimov, “On estimation of the spectral function of a stationary Gaussian process”, Theory Probab. Appl., 8:4 (1963), 366–401 | DOI | MR | Zbl

[18] I. A. Ibragimov, “A central limit theorem for a class of dependent random variables”, Theory Probab. Appl., 8:1 (1963), 83–89 | DOI | MR | Zbl

[19] I. A. Ibragimov, “On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition. I. Necessary conditions”, Theory Probab. Appl., 10:1 (1965), 85–106 | DOI | MR | Zbl

[20] I. A. Ibragimov, “A class of estimates for the spectral function of a stationary sequence”, Theory Probab. Appl., 10:1 (1965), 123–126 | DOI | MR | Zbl

[21] I. A. Ibragimov, “On the accuracy of Gaussian approximation to the distribution functions of sums of independent random variables”, Theory Probab. Appl., 11:4 (1966), 559–579 | DOI | MR | Zbl

[22] I. A. Ibragimov, “On the Chebyshev–Cramér asymptotic expansions”, Theory Probab. Appl., 12:3 (1967), 455–469 | DOI | MR | Zbl

[23] I. A. Ibragimov, “On a theorem of G. Szegö”, Math. Notes, 3:6 (1968), 442–448 | DOI | MR | Zbl

[24] I. A. Ibragimov, “Completely regular multidimensional stationary processes with discrete time”, Proc. Steklov Inst. Math., 111 (1970), 269–301 | MR | Zbl

[25] I. A. Ibragimov, “On the spectrum”, Theory Probab. Appl., 15:1 (1970), 23–36 | DOI | MR | Zbl

[26] I. A. Ibragimov, “Properties of sample functions for stochastic processes and embedding theorems”, Theory Probab. Appl., 18:3 (1974), 442–453 | DOI | MR | Zbl

[27] I. A. Ibragimov, “A note on the central limit theorems for dependent random variables”, Theory Probab. Appl., 20:1 (1975), 135–141 | DOI | MR | Zbl

[28] I. A. Ibragimov, “On smoothness conditions for trajectories of random functions”, Theory Probab. Appl., 28:2 (1984), 240–262 | DOI | MR | Zbl

[29] I. A. Ibragimov, “Some limit theorems for functions of a random walk”, Soviet Math. Dokl., 29:3 (1984), 627–630 | MR | Zbl

[30] I. A. Ibragimov, “Théorèmes limites pour les marches aléatoires”, École d'été de probabilités de Saint-Flour XIII – 1983, Lecture Notes in Math., 1117, Springer, Berlin, 1985, 199–297 | DOI | MR | Zbl

[31] I. A. Ibragimov, “Conditions for Gaussian homogeneous fields to belong to classes”, J. Math. Sci. (N. Y.), 68:4 (1994), 484–497 | DOI | MR | Zbl

[32] I. A. Ibragimov, “Remarks on variations of random fields”, J. Math. Sci. (N. Y.), 75:5 (1995), 1931–1934 | DOI | MR | Zbl

[33] I. A. Ibragimov, “On almost-everywhere variants of limit theorems”, Dokl. Math., 54:2 (1996), 703–705 | MR | Zbl

[34] I. Ibragimov, “On estimation of analytic functions”, Studia Sci. Math. Hungar., 34:1-3 (1998), 191–210 | MR | Zbl

[35] I. A. Ibragimov, “On the extrapolation of entire functions observed in a Gaussian white noise”, Ukrainian Math. J., 52:9 (2000), 1383–1395 | DOI | MR | Zbl

[36] I. A. Ibragimov, “An estimation problem for quasilinear stochastic partial differential equations”, Problems Inform. Transmission, 39:1 (2003), 51–77 | DOI | MR | Zbl

[37] I. A. Ibragimov, “Estimation of analytic densities based on censored data”, J. Math. Sci. (N. Y.), 133:3 (2006), 1290–1297 | DOI | MR | Zbl

[38] I. Ibragimov, “Estimation of analytic spectral density of Gaussian stationary processes”, Parametric and semiparametric models with applications to reliability, survival analysis, and quality of life, Stat. Ind. Technol., Birkhäuser Boston, Boston, MA, 2004, 419–443 | DOI | MR | Zbl

[39] I. A. Ibragimov, “On censored sample estimation of a multivariate analytic probability density”, Theory Probab. Appl., 51:1 (2007), 142–154 | DOI | MR | Zbl

[40] I. A. Ibragimov, “On the estimation of an analytic spectral density outside of the observation band”, Topics in stochastic analysis and nonparametric estimation, Papers presented at the conference “Asympototic analysis in stochastic processes, nonparametric estimation, and related problems”, dedicated to professor R. Z. Khasminskii on the occasion on the 75th birthday (Detroit, MI 2006), IMA Vol. Math. Appl., 145, Springer, New York, 2008, 85–103 | DOI | MR | Zbl

[41] I. A. Ibragimov, “On the Ghurye–Olkin–Zinger theorem”, J. Math. Sci. (N. Y.), 199:2 (2014), 174–183 | DOI | MR | Zbl

[42] I. A. Ibragimov, “On the Skitovich–Darmois–Ramachandran theorem”, Theory Probab. Appl., 57:3 (2013), 368–374 | DOI | MR | Zbl

[43] I. A. Ibragimov, “On estimation of the intensity density function of a Poisson random field outside the observation region”, J. Math. Sci. (N. Y.), 214:4 (2016), 484–492 | DOI | MR | Zbl

[44] I. A. Ibragimov, “On estimation of functions of a parameter observed in Gaussian noise”, J. Math. Sci. (N. Y.), 238:4 (2019), 463–470 | DOI | MR | Zbl

[45] I. A. Ibragimov, “An estimation problem for the intensity density of Poisson processes”, J. Math. Sci. (N. Y.), 251:1 (2020), 88–95 | DOI | MR | Zbl

[46] I. Ibragimov, Z. Kabluchko, and M. Lifshits, “Some extensions of linear approximation and prediction problems for stationary processes”, Stochastic Process. Appl., 129:8 (2019), 2758–2782 | DOI | MR | Zbl

[47] I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of generalized Bayes estimates”, Soviet Math. Dokl., 11 (1970), 1181–1185 | MR | Zbl

[48] I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of statistical estimators in the smooth case. I. Study of the likelihood ratio”, Theory Probab. Appl., 17:3 (1973), 445–462 | DOI | MR | Zbl

[49] I. A. Ibragimov and R. Z. Has'minskii (Khas'minskii), “Asymptotic behavior of statistical estimates for samples with a discontinuous density”, Math. USSR-Sb., 16:4 (1972), 573–606 | DOI | MR | Zbl

[50] I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of some statistical estimators. II. Limit theorems for the a posteriori density and Bayes' estimators”, Theory Probab. Appl., 18:1 (1973), 76–91 | DOI | MR | Zbl

[51] I. A. Ibragimov and R. Z. Khas'minskii, “On moments of generalized Bayessian estimators and maximum likelihood estimators”, Theory Probab. Appl., 18:3 (1974), 508–520 | DOI | MR | Zbl

[52] I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of statistical estimators of the location parameter for samples with continuous density with singularities”, J. Soviet Math., 9 (1978), 50–72 | DOI | MR | Zbl

[53] I. A. Ibragimov and R. Z. Has'minskii (Khas'minskii), “Estimation of a signal parameter in Gaussian white Noise”, Problems Inform. Transmission, 10:1 (1974), 31–46 | MR | Zbl

[54] I. A. Ibragimov and R. Z. Has'minskii (Khas'minskii), “Parameter estimation for a discontinuous signal in white Gaussian nsoise”, Problems Inform. Transmission, 11:3 (1975), 203–212 | MR | Zbl

[55] I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density”, J. Soviet Math., 16:2 (1981), 1035–1041 | DOI | MR | Zbl

[56] I. A. Ibragimov and R. Z. Khas'minskii, “A problem of statistical estimation in Gaussian white noise”, Soviet Math. Dokl., 18 (1978), 1351–1354 | MR | Zbl

[57] I. A. Ibragimov and R. Z. Has'minskii (Khas'minskii), Statistical estimation. Asymptotic theory, Appl. Math., 16, Springer-Verlag, New York–Berlin, 1981, vii+403 pp. | DOI | MR | Zbl

[58] I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic bounds on the quality of the nonparametric regression estimation in $\mathscr L_p$”, J. Soviet Math., 24:5 (1984), 540–550 | DOI | MR | Zbl

[59] I. A. Ibragimov and R. Z. Khas'minskii, “Estimation of distribution density”, J. Soviet Math., 21:1 (1983), 40–57 | DOI | MR | Zbl

[60] I. A. Ibragimov and R. Z. Khas'minskii, “More on the estimation of distribution densities”, J. Soviet Math., 25:3 (1984), 1155–1165 | DOI | MR | Zbl

[61] I. A. Ibragimov and R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part I”, Theory Probab. Appl., 43:3 (1999), 370–387 | DOI | DOI | MR | Zbl

[62] I. A. Ibragimov and R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part II”, Theory Probab. Appl., 44:3 (2000), 469–494 | DOI | MR | Zbl

[63] I. A. Ibragimov and R. Z. Khas'minskii, “Estimation problems for coefficients of stochastic partial differential equations. Part III”, Theory Probab. Appl., 45:2 (2001), 210–232 | DOI | MR | Zbl

[64] I. Ibragimov and M. Lifshits, “On the convergence of generalized moments in almost sure central limit theorem”, Stat. Probab. Lett., 40:4 (1998), 343–351 | DOI | MR | Zbl

[65] I. A. Ibragimov and M. A. Lifshits, “On almost sure limit theorems”, Theory Probab. Appl., 44:2 (2000), 254–272 | DOI | DOI | MR | Zbl

[66] I. A. Ibragimov and Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443 pp. | MR | Zbl

[67] I. A. Ibragimov, “On the expected number of real zeros of random polynomials. I. Coefficients with zero means”, Theory Probab. Appl., 16:2 (1971), 228–248 | DOI | MR | Zbl

[68] I. A. Ibragimov and N. B. Maslova, “On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means”, Theory Probab. Appl., 16:3 (1971), 485–493 | DOI | MR | Zbl

[69] I. A. Ibragimov and N. B. Maslova, “Average number of real roots of random polynomials”, Soviet Math. Dokl., 12 (1971), 1004–1008 | MR | Zbl

[70] I. A. Ibragimov, A. S. Nemirovskii, and R. Z. Has'minskii (Khas'minskii), “Some problems on nonparametric estimation in Gaussian white noise”, Theory Probab. Appl., 31:3 (1987), 391–406 | DOI | MR | Zbl

[71] I. A. Ibragimov and L. V. Osipov, “On an estimate of the remainder in Lindeberg's theorem”, Theory Probab. Appl., 11:1 (1966), 125–128 | DOI | MR | Zbl

[72] I. A. Ibragimov and S. S. Podkorytov, “Random real algebraic surfaces”, Dokl. Math., 52:1 (1995), 101–103 | MR | Zbl

[73] I. A. Ibragimov, E. L. Presman, and Sh. K. Formanov, “On modifications of the Lindeberg and Rotar' conditions in the central limit theorem”, Theory Probab. Appl., 65:4 (2021), 648–651 | DOI | DOI | MR | Zbl

[74] I. A. Ibragimov and Y. A. Rozanov, Gaussian random processes, Appl. Math. (N. Y.), 9, Springer-Verlag, New York–Berlin, 1978, x+275 pp. | MR | Zbl

[75] I. A. Ibragimov and V. N. Solev, “The asymptotic behavior of the prediction error of a stationary sequence with a spectral density of special type”, Theory Probab. Appl., 13:4 (1968), 703–707 | DOI | MR | Zbl

[76] I. A. Ibragimov and V. N. Solev, “A condition for regularity of a Gaussian stationary process”, Soviet Math. Dokl., 10 (1969), 371–375 | MR | Zbl

[77] I. A. Ibragimov and V. N. Solev, “A condition for the regularity of a stationary Gaussian sequence”, Semin. Math., 12, V. A. Steklov Math. Inst., Leningrad, 1971, 54–60 | MR | Zbl

[78] I. Ibragimov and D. Zaporozhets, “On distribution of zeros of random polynomials in complex plane”, Prokhorov and contemporary probability theory, In honor of Yu. V. Prokhorov on the occasion of his 80th birthday, Springer Proc. Math. Stat., 33, Springer, Heidelberg, 2013, 303–323 | DOI | MR | Zbl

[79] I. Ibragimov and O. Zeitouni, “On roots of random polynomials”, Trans. Amer. Math. Soc., 349:6 (1997), 2427–2441 | DOI | MR | Zbl

[80] M. Kac, “On the average number of real roots of a random algebraic equation”, Bull. Amer. Math. Soc., 49 (1943), 314–320 | DOI | MR | Zbl

[81] M. Kac, “On the average number of real roots of a random algebraic equation (II)”, Proc. London Math. Soc. (2), 50 (1948), 390–408 | DOI | MR | Zbl

[82] M. Kac, “Toeplitz matrices, translation kernels and a related problem in probability theory”, Duke Math. J., 21:3 (1954), 501–509 | DOI | MR | Zbl

[83] A. N. Kolmogorov and Yu. A. Rozanov, “On strong mixing conditions for stationary Gaussian processes”, Theory Probab. Appl., 5:2 (1960), 204–208 | DOI | MR | Zbl

[84] V. A. Kotel'nikov, Theory of potential noise immunity, Gosenergoizdat, Moscow–Leningrad, 1956, 153 pp. (Russian)

[85] J. E. Littlewood and A. C. Offord, “On the number of real roots of a random algebraic equation”, J. London Math. Soc., 13:4 (1938), 288–295 | DOI | MR | Zbl

[86] J. E. Littlewood and A. C. Offord, “On the number of real roots of a random algebraic equation. II”, Proc. Cambridge Philos. Soc., 35:2 (1939), 133–148 | DOI | Zbl

[87] J. E. Littlewood and A. C. Offord, “On the number of real roots of a random algebraic equation (III)”, Mat. Sb., 12(54):3 (1943), 277–286 | MR | Zbl

[88] L. V. Mamai, “On the theory of characteristic functions”, Sel. Transl. Math. Stat. Probab., 4 (1963), 153–170 | MR | Zbl

[89] A. Nemirovski, “Topics in non-parametric statistics”, Lectures on probability theory and statistics, École d'été de probabilités de Saint-Flour XXVIII – 1998 (Saint-Flour 1998), Lecture Notes in Math., 1738, Springer, Berlin, 2000, 85–277 | DOI | MR | Zbl

[90] B. Ramachandran, Advanced theory of characteristic functions, Statist. Publ. Soc., Calcutta, 1967, vii+208 pp. | MR | Zbl

[91] M. Rosenblatt, “A central limit theorem and a strong mixing condition”, Proc. Nat. Acad. Sci. U.S.A., 42 (1956), 43–47 | DOI | MR | Zbl

[92] P. Schatte, “On strong versions of the central limit theorem”, Math. Nachr., 137 (1988), 249–256 | DOI | MR | Zbl

[93] V. P. Skitovich, “One property of normal distribution”, Dokl. Akad. Nauk SSSR, 89:2 (1953), 217–219 (Russian) | MR | Zbl

[94] V. P. Skitovič, “Linear combinations of independent random variables and the normal distribution law”, Sel. Transl. Math. Stat. Probab., 2 (1962), 211–228 | MR | Zbl

[95] G. Szegő, “On certain Hermitian forms associated with the Fourier series of a positive function”, Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.], 1952, Tome Suppl. (1952), 228–238 | MR | Zbl

[96] D. N. Zaporozhets and I. A. Ibragimov, “On random surface area”, J. Math. Sci. (N. Y.), 176:2 (2011), 190–202 | DOI | MR | Zbl

[97] A. A. Zinger, “On a characterization of the multi-dimensional normal law by the independence of linear statistics”, Theory Probab. Appl., 24:2 (1979), 388–392 | DOI | MR | Zbl