ILDAR ABDULLOVICH IBRAGIMOV

摘要

I. A. Ibragimov turned 80 on July 15, 2012. Ildar Abdullovich is a worldwide renowned mathematician, one of the leading specialists in Probability and Statistics. I. A. Ibragimov is the author of four monographs; he heads a school of Probability and Statistics recognized in the world. Starting from his student years and till now he has been a leading researcher in this field. I. A. Ibragimov introduced and studied in detail conditions of uniformly strong mixing; he proved the Central Limit Theorem for sums of weakly dependent random variables. In the spectral theory of stationary random processes, he indicated a connection between the property of total regularity of processes and the smoothness of the spectral density. In the domain of classical limit theorems, I. A. Ibragimov obtained necessary and sufficient conditions for power rate of convergence in the Central Limit Theorem for sums of i.i.d. random variables and necessary conditions under which the Chebyshev-Cramer asymptotic expansions are valid. He developed a new effective method of asymptotic analysis of functional of random walks. His extremely fruitful collaboration with R. Z. Khasminskii lead to development of the asymptotic theory of statistical estimation for irregular families of distributions. The asymptotic model of a signal in white noise studied by I. A. Ibragimov and R. Z. Khasminskii became canonical in problems of nonparametric estimation and hypotheses testing. I. A. Ibragimov got deep results on estimation of analytic functions in statistical models and analytic spectral densities for Gaussian stationary processes. One of his new papers is published in this volume.