Ildar Ibragimov . Five Decades in Probability and Statistics

Plan 1. Linnik and creation of the Leningrad school 2. Linnik’s students 3. 1951 4. Unimodal distributions 5. Classical limit theorems a) moment conditions for given convergence rate b) fast convergence rates in CLT c) Chebyshev-Cramér asymptotic expansions 6. Weak dependence a) uniform mixing condition b) central limit theorem under uniform mixing condition c) continued fractions d) central limit theorem for martingale differences e) book: Ibragimov and Linnik 7. Spectral theory of random processes a) Toeplitz matrices b) total regularity c) book: Ibragimov and Rozanov 8. Functionals of random walk a) St-Flour lectures b) book: Borodin and Ibragimov 9. Smoothness of sample paths 10. Zeros of random polynomials 11. Statistical estimation a) normality of estimates in parametric models b) sequential estimation c) estimation in white noise model d)book: Ibragimov and Khasminskii e) estimation in nonparametric models 12. Recent works a) almost sure limit theorems b) estimation of SPDE coefficients 13. Ibragimov’s students 14. Awards