Veretennikov

Alexander Yurievich

Head of lab for stochastic dynamical systems, Institute for Information Transmission Problems, Russian Academy of Sciences (1997);

Professor, Probability Department, Mechanics and Mathematics Faculty of Moscow University (1994);

Graduated from Moscow University (1975), Probability Department, scientific advisor A.D.Solov'ev; Ph.D. (kandidat of sciences) (1979), scientific advisor -- N.V.Krylov; Senior Research Fellow (1983); Dr.Sci. (1991); Professor (1997)
e-mail: veretenn@iitp.ru; ayu@sci.lebedev.ru

Scientific interests:: stochastic differential equations, large deviations, averaging, homogenization, mixing, stochastic algorithms, applications on statistics, ill-posed problems, PDEs.

Non-scientific interests: classical music, skiing, kayaking, rafting,
laureate of Moscow amateur art competitions, piano,
1-st degree and instructor title on rafting and kayaking (1990).

Theses:

• Ph.D.- "Weak and strong solutions of stochastic differential equations", 1979, Moscow University, Committee head A.N.Kolmogorov, scientific supervisor N.V.Krylov, referees A.N.Shiryaev, A.K.Zvonkin
• Dr.Sci.-"Study of large deviations, averaging principle and mixing rate for systems of stochastic differential equations", 1990, Mathematical Institute of USSR Academy of Sciences (Steklov), Committee head Yu.V.Prokhorov, referees B.Grigelionis, A.V.Skorokhod, A.N.Shiryaev.

Advanced courses: stochastic analysis; SDEs; large deviations; statistics of stochastic processes; recurrent Markov chains

Topics for diploma and theses:

- mixing rates for Markov and stationary processes
- large and moderate deviations for service processes
- estimation efficiency for Markov experiments
- stochastic approximation in parameter estimation
- adaptive estimation of unknown density
- approximation methods for PDEs

Participance in some Russian projects:

- project RFBR "Study of large deviations in stochastic systems", 1993-1994
- project RFBR "Asymptotical analysis for stochastic averaged systems", 1995-1997
- project RFBR "Averaging and diffusion approximation for stochastic systems with a small parameter", 1998-2000
- project RFBR "Algorithms of statistical estimation with averaging: convergence rate and information bounds", 1998-2000

Participance in some European projects for Russia:

- with Warwick University, K.D.Elworthy, INTAS project "Stochastic analysis and its applications" (1994-1999)
- with INRIA/IRISA, Rennes, France, A.Benveniste, INTAS project "Nonparametric identification of dynamical systems: optimal and adaptive algorithms" (1993-1997)
- with Universite de Provence, E.Pardoux, P.Mathieu, projects CNRS "Homogenization and large deviations" (1997), "Homogenization, averaging and random media: probability methods and applications" (1999)

Awards:

- State stipendium "For outstanding scientists of Russia", 1994-1996, 1997-1999,
- prize of Russian foundation "Mathematics" 1992.

Invited lectures:

(1986) 1 World Bernoulli Soc. Congress (Tashkent), "Malliavin calculus and its applications to some limit theorems"
(1995) Journees de Statistique, France, "On stochastic algorithms and large deviations"
(1997) Mathematical statistics and its applications in biosciences, Bernoulli and ISI-meeting, Rostock, Germany, "On large deviations for stochastic approximation algorithms with a constant gain finction"
(1998) 7th Vilnius Conference on Probability Theory and Mathematical Statistics, "On large deviations for averaged diffusions"

Lecture notes:

1. Beginning of Probability Theory - 1, MIREA, 1994 (in Russian),
2. Beginning of Probability Theory - 2 (with E.V.Veretennikova), MIREA, 1997 (in Russian).

Monographs::

1. (with G.M.Vainikko) Iteration procedures in ill-posed problems. Nauka, Moscow, 1986 (in Russian).
2. (with S.V.Anulova, N.V.Krylov, R.Sh.Liptser, A.N.Shyriaev) Probability III. Stochastic Calculus. VINITI, Moscow, ser. Fundamental studies, vol. 35, 1989 (in Russian).
3. (with O.V.Gulinsky) Large deviations for discrete-time processes with averaging. VSP, Utrecht, The Netherlands, 1993.
4. (with S.V.Anulova, N.V.Krylov, R.Sh.Liptser, A.N.Shyriaev) Probability III. Stochastic Calculus. Springer, Berlin, 1998 [translation of 2].

Some papers:

[1] (with N.V.Krylov) Explicit formulas for solutions of stochastic equations. Math. USSR Sborn. 1976, 29(2), 239-256.
[2] Ergodicity of service systems with an infinite numbers of servomechanisms. Math. Notes. 1977, 22(3-4), 804-808.
[3] On strong solutions and explicit formulas for solutions of stochastic integral equations. Math. USSR Sborn. 1981, 39(3), 387-403.
[4] (with I.V.Emelin and M.A.Krasnosel'skii) On regularization of ill-posed problems by stop-rules of iterative procedures with random errors. Numer. Funct. Anal. and Optimiz. 1983, 5(2), 199-215.
[5] A probabilistic approach to hypoellipticity. Russ. Math. Surveys. 1983, 38(3), 127-140.
[6] (with M.L.Kleptsina) On strong solutions of stochastic Ito-Volterra equations. Theory Probab. Appl. 1984, 29(1), 154-158.
[7] Bounds for the mixing rate in the theory of stochastic equations. Theory Probab. Appl. 1987, 32(2), 273-281.
[8] On the averaging principle for systems of stochastic differential equations. Math. USSR Sborn., 1991, 69(1), 271-284.
[9] Veretennikov, A.Yu. (1991) On the Estimates of the Mixing Rate for Markov Processes. Lietuvos Matem. Rink. 31, 1, 40-49 (in Russian)
[10] On large deviations in the averaging principle for stochastic differential equations with periodic coefficients. 2. - Math. USSR Izveztia. 1992, 39(1), 677-701.
[11] Large deviations in averaging principle for stochastic differential equation systems (noncompact case). Stochastics and Stochastics Reports, 1994, 48, 83-96.
[12] On large deviations for diffusion processes with measurable coefficients, Russian Math. Surveys, 1995, 50(5), 135-146 (in Russian)
[13] Lower bound for large deviations for an averaged SDE with a small diffusion, Russian Journal of Mathematical Physics, 1997, 5(1), 99-104.
[14] (with E.Pardoux) Averaging of backward stochastic differential equations, with application to semi-linear PDE's, Stochastics and Stochastics Reports, 1997, 60, 255-270.
[15] (with P.Priouret) A remark on the stability of the l.m.s. tracking algorithm, Stochastic Analysis and its Applications, 16(1), 118-128.
[16] On large deviations for stochastic differential equations with a small diffusion and averaging, Probab. Theory Appl., 1998, 43(2), 349-351 (in Russian)
[17] On large deviations in the averaging principle for SDE's with a "full dependence", Probab. Theory Appl., 1998, 43(4), 765-767 (in Russian)

Some preprints:

1. On a Castellana-Leadbetter condition for a diffusion process density estimation; preprint 96-2 Univ. du Maine et d'Angers (accepted to "Stoch. Inference for Stoch. Processes")
2. On parameter estimation for ergodic Markov chains with unbounded loss functions, WIAS, Berlin, 1998, preprint 448; preprint@wias-berlin.de and http://www.wias-berlin.de/
3. (with E.Pardoux) On Poisson equation and diffusion approximation, 1. prepublication ATP CMI Univ. de Provence, 98-14.