A. Veretennikov - Publications

2016

Veretennikov A., Kleptsyna M.L., On robustness of discrete time optimal filters, Mathematical Methods of Statistics (ISSN: 1066-5307 (Print) 1934-8045 (Online)), 2016, 25(3), 207-218. http://link.springer.com/journal/12004/25/3/page/1; doi:10.3103/S1066530716030042
Veretennikov A., Veretennikova E.V., On partial derivatives of multivariate Bernstein polynomials, Siberian Advances in Mathematics (ISSN 1055-1344), 2016, 26(4), 231-242.
Veretennikov A., On Recurrence and Availability Factor for Single–Server System With General Arrivals, Reliability: Theory and Applications (RT&A), 2016, vol.11, #3(42), 49-58. (http://www.gnedenko-forum.org/Journal/2016_3.htm) http://www.gnedenko-forum.org/Journal/2016/032016/RTA_3_2016-06.pdf
Veretennikov A., Zverkina G.A., On Polynomial Bounds of Convergence for the Availability Factor, Chapter in: Distributed Computer and Communication Networks, Volume 601 of the series Communications in Computer and Information Science, Springer, 2016, pp 358-369. DOI 10.1007/978-3-319-30843-2_37 http://link.springer.com/chapter/10.1007%2F978-3-319-30843-2_37
Veretennikov A., Bogachev V.I., Shaposhnikov S.V., Veretennikov A.Yu. Differentiability of solutions of stationary Fokker-Planck-Kolmogorov equations with respect to a parameter, Discrete and Continuous Dynamical Systems - Series A, 36, 3519-3543, 2016. DOI:10.3934/dcds.2016.36.3519; http://bibos.math.uni-bielefeld.de/preprints/15-05-487.pdf http://dx.doi.org/10.3934/dcds.2016.36.3519
Veretennikov A., G. Da Prato, F. Flandoli, M. Röckner, and A. Yu. Veretennikov, Strong uniqueness for SDEs in Hilbert spaces with nonregular drift, Ann. Probab. Volume 44, Number 3 (2016), 1985-2023. https://aps.arxiv.org/abs/1404.5418 http://iitp.ru/https://projecteuclid.org/euclid.aop/1463410037

2015

Veretennikov A., Zverkina G., ON POLYNOMIAL CONVERGENCE RATE OF THE AVAILABILITY FACTOR TO ITS STATIONARY VALUE, http://www.dccn2015.com/uploads/submitted_papers/Veretennikov_Zverkina.pdf

2014

Veretennikov A., A.Yu. Veretennikov and G.A. Zverkina, Simple Proof of Dynkin’s Formula for Single-Server Systems and Polynomial Convergence Rates, Markov Processes Relat. Fields 20 (2014), 479–504.
Veretennikov A., R. Abu-Shanab, A. Yu. Veretennikov, On asymptotic Borovkov-Sakhanenko inequality with unbounded parameter set, Teor. Imovir. Ta Matem. Statyst., No 90, 2014, pp.1-12; Theor. Probability and Math. Statist. 90 (2015), 1-12. http://probability.univ.kiev.ua/tims/issues-new/90/PDF/3.pdf
Veretennikov A., S. Anulova, A. Veretennikov, Exponential Convergence of degenerate Hybrid Stochastic Systems with full Dependence, in: Modern Stochastics and Applications, Springer, Optimization and Its Applications 90, Springer International Publishing Switzerland 2014, 159-174. DOI: 10.1007/978-3-319-03512-3_10

2013

Veretennikov A., S. V. Anulova, A. Yu. Veretennikov, and P. S. Shcherbakov, Exponential Convergence of Multi-Dimensional Stochastic Mechanical Systems with Switching. Proc. 52nd IEEE Conference on Decision and Control, December 10-13, Florence, Italy, 2013, 1217-1222 ( 1807.pdf). ISBN: 978-1-4673-5716-6.
Veretennikov A., Butkovsky O.A., On asymptotics for Vaserstein coupling of Markov chains, Stochastic Processes and their Applications, 123(9), 2013, 3518-3541.
Veretennikov A., On large deviations in the averaging principle for SDE’s with a ``full dependence’’, revisited // Discrete and Continuous Dynamical Systems ser. B, 2013. V. 18. No. 2. P. 523-549. (doi: 10.3934/dcdsb.2013.18.523) http://probability.univ.kiev.ua/tims/issues-new/90/PDF/3.pdf

2011

Veretennikov A., On Sobolev Solutions of Poisson Equations in R^d with a Parameter (To 70th birthday of Professor N.V.Krylov), Journal of Mathematical Sciences, 179(1), 48-79, 2011 (Eng); О соболевских решениях уравнения Пуассона в R^d с параметром (К 70-летию профессора Н.В.Крылова), Проблемы математического анализа, 61, 43-68, 2011.
Veretennikov A., (With O.A.Butkovsky) On asymptotics of Vaserstein"s coupling for a Markov chain. International Mathematical Conference "50 years of IPPI", July 25-29 2011 Moscow, Russia, Proceedings, ISBN 978-5-901158-15-9 http://www.iitp.ru/ru/conferences/839.htm
Veretennikov A., (With S.V.Anulova) On ergodicity of highly degenerate hybrid stochastic control systems. International Mathematical Conference "50 years of IPPI", July 25-29 2011 Moscow, Russia, Proceedings, ISBN 978-5-901158-15-9 http://www.iitp.ru/ru/conferences/839.htm/
Veretennikov A., M.L.Kleptsyna, On filtering with unspecified initial data for nonuniformly ergodic signams, in: The Oxford Handbook of nonlinear filtering, D.Crisan and B.Rozovsky (Eds.), Oxford University Press, Oxford, 2011, 267-298.

2010

Veretennikov A., (with S.V.Anulova) On ergodic properties of degenerate hybrid stochastic control systems, in: Decision and Control (CDC), 2010 49th IEEE Conference on Issue Date: 15-17 Dec. 2010 On page(s): 2292 - 2297 Location: Atlanta, GA ISSN: 0743-1546 Print ISBN: 978-1-4244-7745-6 INSPEC Accession Number: 11848709 Digital Object Identifier: 10.1109/CDC.2010.5717412 http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5717412
Veretennikov A., О скорости перемешивания и сходимости к стационарному распределению в систеах типа Эрланга в непрерывном времени, Проблемы передачи информации, 2010, №4, стр.122-129. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ppi&paperid=2030&option_lang=rus
Veretennikov A., Abourashchi N., On stochastic averaging and mixing, Theory of Stochastic Processes, 16(32)(1) (2010), 111-130. URL of preprint version below. http://iitp.ru//upload/userpage/94/ayvlvov09c.pdf
Aivaliotis G., Veretennikov A., On Bellman"s equations for mean and variance control of a Markov diffusion, Stochastics: An International J. of Probability and Stochastic Processes, Electronic version: 82 (6 Nov 2009), pages unknown. Printed version: Volume 82, Issue 1 February 2010 , pages 41 - 51 DOI: 10.1080/17442500902723567. http://www.tandfonline.com/doi/abs/10.1080/17442500902723567#preview
Kleptsyna M., Veretennikov A., On discrete time ergodic filters with wrong initial data, 2, Stochastics: An International J. of Probability and Stochastic Processes, Electronic online version: 82 (01 Sept 2009), pages unknown. Printed version: Volume 82, Issue 1 February 2010 , pages 25 - 40; DOI: 10.1080/17442500902723559 http://www.tandfonline.com/doi/abs/10.1080/17442500902723559#preview

2009

Veretennikov A., N. Abourashchi, A.Yu. Veretennikov, On Weak solutions and local Dobrushin"s mixing condition for 2D degenerate stochastic differential equations. In: Proc. Internat. Dobrushin conference, July 15-20 2009, Moscow, ISBN 978-5-901158-10-4, p. 5-11. http://iitp.ru/www.iitp.ru/upload/content/347/Dobr_Conf_2009_Proceedings.pdf
Veretennikov A., (with N.Abourashchi) On exponential mixing bounds and convergence rate for reciprocal Gamma diffusion processes, Mathematical Communications, 14(2) (2009), 331-339. http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=68541&lang=en

2008

Kleptsyna M., Veretennikov A., On discrete time filtres with wrong initial data, Probability Theory and Related Fields (2008) 141:411–444. http://www.springerlink.com/content/f3529k62w5h3811r/
Veretennikov A., Kleptsyna M., A. Yu. Veretennikov, M. L. Kleptsyna, “On Continuous Time Ergodic Filters with Wrong Initial Data”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 240–276 http://www.mathnet.ru/php/journal.phtml?wshow=paper&jrnid=tvp&paperid=2408&year=2008&volume=53&issue

2007

Kleptsyna M., Veretennikov A., On ergodic filters with wrong initial data, C.R.Acad. Sci. Paris, Ser. I, 344(2007), 727-731.
Veretennikov A., On asymptotic information integral inequalities. (English) Theory Stoch. Process. 13, No. 29, Part 1-2, 294-307 (2007).

2006

Veretennikov A., On ergodic measures for McKean--Vlasov stochastic equations, In: Monte Carlo and Quasi-Monte Carlo Methods 2004 Niederreiter, H; Talay, D. (Eds.), (2006), 471-486. http://www.springerlink.com/content/u04780308x116512/
Veretennikov A., On lower bounds for mixing coefficients of Markov diffusions, In: From Stochastic Calculus to Mathematical Finance; The Shiryaev Festschrift. Kabanov, Yu.; Liptser, R.; Stoyanov, J. (Eds.) Springer, Berlin et al. (2006), 623--633. http://www.springerlink.com/content/m524n00329448147/
Veretennikov A., Совместно с С.А.Клоковым. Mixing and convergence rates for a family of Markov processes approximating SDEs, ROSE - Random Oper. and Stoch. Equ., 14(2) (2006), 103-126. http://www.xolopo.com/mathematics/mixing_convergence_rates_a_family_markov_processes_17253.html

2005

Veretennikov A., Совместно с E.Pardoux. On the Poisson equation and diffusion approximation 3. Ann. Probab. 33(3) (2005), 1111-1133.

2004

Veretennikov A., Approximations for ergodic SDEs, Summer School 2004 Lecture notes, Helsinki University of Technology Institute of Mathematics Reports C-17 http://math.tkk.fi/visitors0405/AVslides.pdf
Veretennikov A., (with Zhizhina, E.A.) On stochastic algorithms for the global optimization problem on a compact. In R.G. Aykroyd, S. Barber, & K.V. Mardia (Eds.), Bioinformatics, Images, and Wavelets, pp. 77-81. Department of Statistics, University of Leeds. http://www1.maths.leeds.ac.uk/Statistics/workshop/lasr2004/Proceedings/veretennikov-revised.pdf
Veretennikov A., With S.A.Klokov. Subexponential mixing rate for a class of Markov diffusions, J. Math. Sci. 123(1) (September 2004), 3816-3823. (http://www.springerlink.com/content/u831516785838223/ but the article is not available)
Veretennikov A., With S.A.Klokov. Sub-exponential mixing rate for a class of Markov processes, Math. Comm. 9 (2004), 9-26. http://hrcak.srce.hr/index.php?show=clanak_download&id_clanak_jezik=1422

2003

Veretennikov A., On large deviations for approximations of SDEs, Probab. Theory Rel. Fields, 125(1) (2003), 135-152.
Veretennikov A., On approximate large deviations for 1D diffusion. Dedicated to the memory of Professor Revaz Chitashvili. Georgian Math. J. 10(2) (2003), 381--399.
Veretennikov A., Совместно с E.Pardoux. On Poisson equation and diffusion approximation 2, Annals of Probability, 31(3) (2003), 1166--1192. http://www.jstor.org/pss/3481484

2002

Veretennikov A., With A.B.Varakin. On parameter estimation for ``polynomial ergodic"" Markov chains with polynomial growth loss functions, Markov Processes and Related Fields, 8(1) (2002), 127-144.
Veretennikov A., With R.Liptser and V.Spokoiny. Freidlin--Wentzell type large deviations for smooth processes, Markov Processes Rel. Fields, 8 (2002), 611-636.
Veretennikov A., Coupling method for Markov chains under integral Doeblin type condition. Theory Stoch. Process. 8(24) (2002), no.3-4, 383-390.

2001

Veretennikov A., With E.Pardoux. On the Poisson equation and diffusion approximation. I. Ann. Probab. 29(3) (2001), 1061--1085.

2000

Veretennikov A., On large deviations for SDEs with small diffusion and averaging. Stochastic Process. Appl. 89(1) (2000), 69-79
Veretennikov A., With G.N.Milstein. On deterministic and stochastic sliding modes via small diffusion approximation. Markov Process. Related Fields 6(3) (2000), 371-395

1999

Veretennikov A., On KPP equations with various wave front speeds, the Larson result via large deviations, in: Probability Theory and Mathematical Statistics: Proceedings of the 7th Vilnius Conference (1998) Vilnius, Lithuania (12-18 August, 1998), TEV, Vilnius, Lithuania, and VSP, Utrecht, the Netherlands & Tokyo, Japan, 1999, 707-714
Veretennikov A., On Castellana--Leadbetter"s Condition for Diffusion Density Estimation, Statistical Inference for Stochastic Processes, 2(1), 1-9 http://www.springerlink.com/content/r5p16r007628k533/
Veretennikov A., On large deviations in the averaging principle for SDE"s with a "full dependence", Ann. Probab. 1999, 27(1), 284-296

1998

Veretennikov A., On parameter estimation for ergodic Markov chains with unbounded loss functions. WIAS, Berlin, 1998, preprint 448. (Version of the paper in MPRF 2002.) http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55.7889&rep=rep1&type=pdf
Veretennikov A., (with Anulova, S.V., Krylov, N.V., Liptser, R.S., Shyriaev, A.N.) Probability III. Stochastic Calculus. Berlin: Springer.
Veretennikov A., (with P.Priouret) A remark on the stability of the l.m.s. tracking algorithm, Stoch. Anal. Appl. 16(1) (1998), 118-128

1997

Veretennikov A., (with E.Pardoux) Averaging for backward stochastic differential equations, with applications to semi-linear PDE"s, Stoch. Stoch. Rep. 60 (1997), 255-270.
Veretennikov A., On polynomial mixing bounds for stochastic differential equations, Stoch. Processes Appl. 70 (1997), 115-127
Veretennikov A., (with M.Kelbert) On the estimation of mixing coefficients for a multiphase service systems, Queueing Systems and Applications (QUESTA), 25, 325-337

1996

Veretennikov A., On polynomial mixing bounds for stochastic differential equations, IRISA, publication interne no 1026. (Extended version of the paper in SPA 1997) http://iitp.ru/https://www.irisa.fr/doccenter/publis/PI/1996/irisapublication.2006-02-16.8300043499
Veretennikov A., On large deviations for SDE systems without bounded coefficient derivatives, Stoch. Anal. and Appl., Proc. 5th Gregynog Symp., Gregynog, Powys, 9-14 July 1995, Publ.Co. World Sci. Press, 1996, 471-478
Veretennikov A., On large deviations for stationary processes under local ratio-mixing conditions, Uspehi Teorii Veroyatnostej i ee Primenenij, Proc. 4th Russian-Finnish Symp. on Probability Theory and Mathematical Statistics (3-8 oct. 1993, Moscow), ed. by A.N.Shiryaev et al., TVP, Moscow, 1996, 217-222

1995

Veretennikov A., On backward filtering equations for SDE systems (direct approach). In: Stochastic Partial Differential Equations, ed. by A.Etheridge. London Math. Soc. Lecture Notes Series, Cambridge Univ. Press, vol. 216 (1995), 304-311

1994

Veretennikov A., On large deviations in averaging principle for systems of stochastic differential equations with unbounded coefficients. Probability Theory and Mathematical Statistics. Proc. Sixth Vilnius Conf. (28 June - 3 July, 1993). Ed. B.Grigelionis et al. VSP, Utrecht, The Netherlands and Tokyo, Japan
Veretennikov A., On large deviations for diffusion processes under minimal smoothness conditions. C.R.Acad.Sci Paris, ser. Matem, vol. 319, Ser. A, N 7, Oct. 1994, 727-732
Veretennikov A., Large deviations in averaging principle for stochastic differential equation systems (noncompact case). Stochastics and Stochastics Reports, 1994, 48, 83-96.
Veretennikov A., On large deviations and averaging principle for stochastic - difference equation on a torus. Proc. Steklov Inst. of Math., (1994), Issue 4, 27--33.
Veretennikov A., On large deviations in averaging principle for systems of stochastic differential equations with unbounded coefficients. Probability Theory and Mathematical Statistics. Proc. Sixth Vilnius Conf. (28 June - 3 July, 1993). Ed. B.Grigelionis et al. VSP, Utrecht, The Netherlands and Tokyo, Japan, 1994, 735-742
Veretennikov A., On weak Bernoulli, mixing rate and large deviations for SDE"s and stochastic difference systems with averaging. Proc. Internat. Workshop on Stochastic Partial Differential Equations (Univ. of North Carolina, Chapel Hill, NC, June 19-21, 1994), part 2, 5 pages (non-refereed extended abstract).

1993

Veretennikov A., Совместно с О.В.Гулинским (O.V.Gulinsky), Large deviations for discrete - time processes with averaging. VSP, Utrecht, The Netherlands.

1992

Veretennikov A., On large deviations for ergodic process empirical measures. Advances in Soviet Math. Vol. 12, 125-133 (this Journal exists only in English).
Veretennikov A., On asymptotic properties of stationary processes: large deviations and exponential mixing. Proc. VI Soviet - Japan Symp. on Probab. Theory and Mathem. Stat. (Kiev, 1991). World Scientific, Singapore et al. 1992, 403-413
Veretennikov A., On large deviations for stochastic iterative procedures in Hilbert space. Numerical Methods and Optimization, Vol.3. Tallinn: Estonian Academy of Sciences, 1992, 88-96

1990

Veretennikov A., (with O.V.Gulinskii) Rate of mixing and the averaging principle for stochastic recursive procedures. Aut. Remote Control. 51(6), 779-788
Veretennikov A., On large deviations in averaging principle for stochastic differential equations with periodic coefficients. 1. - Probab. Theory and Math. Statistics. Proc. Fifth Vilnius Conf. (1989). Ed. by B.Grigelionis et. al.Vilnius, Lithuania: Mokslas and Utrecht, The Netherlands: VSP, Vol. 2, 542-551

1989

Veretennikov A., Optimal stabilization of controllable random processes with fast oscillating noise. Aut. Remote Control, 50(8), 1061-1065
Veretennikov A., Probability density of stochastic differential equations. In: Statistics and Control of Stochastic Processes. Steklov seminar 1985-1986. Vol. 2. Ed. by A.N.Shiryaev et al. N.Y. Optimization Software, Inc. Publ. Divizion. 233-237

1988

Veretennikov A., Rate of convergence of stochastic iteration procedures in ill - posed problems. Aut. Remote Control. 49(1), 56-60

1987

Veretennikov A., Malliavin calculus and its applications to some limit theorems. Proc. 1 - st World Congress Bernoully Soc., Tashkent, 1986. Vol. 1. Utrecht: VNU Sci. Press. 557-566
Veretennikov A., Lower bound for large deviations for an averaged SDE with a small diffusion, Russian Journal of Mathematical Physics, 1997, 5(1), 99-104.

1986

Veretennikov A., Regularization of ill-posed problems by stochastic iteration procedures in the mean. Aut. Remote Control. 47(10), 1367-1372

1985

Veretennikov A., (with M.L.Kleptsina) On filtering and properties of conditional laws of Ito-Volterra processes, Statistics and Control of Stochastic Processes, 1985. Steklov seminar, 1984. Ed. by N.V.Krylov et al. Optimiz. Software, Publ. divizion, N.Y. 179-196

1984

Veretennikov A., Iterative methods in ill-posed problems with random errors. Aut. Remote Control. 45(12), 1564-1569

1983

Veretennikov A., On the criteria for the existence of a strong solution of a stochastic equation. Theory Probab. Appl. 27(3), 441-449
Veretennikov A., (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.

1981

Veretennikov A., On strong and weak solutions of one - dimensional stochastic equations with boundary conditions. Theory Probab. Appl. 26(4), 670-686 http://mi.mathnet.ru/tvp3500
Veretennikov A., Ergodicity and invariance principle for multiphase queuing systems. Aut. Remote Control. 42(7), 906-909

1980

Veretennikov A., On the existence of the optimal policy for a multidimensional quasidiffusion controlled process. Lecture Notes in Control and Information Sci., Springer, vol. 25, 80-90

1978

Veretennikov A., On the existence of the optimal strategy in a diffusion process control problem. Internat. Symp. Stoch. Diff. Equations, Vilnius, 1978. Abstr. comm., 174-177