Small ball probabilities

Small deviations of sums of correlated stationary Gaussian sequences (joint with F.Aurzada). Theory Probab. Appl., 2016, 61, no. 4, 626-658 (in Russian), 

Small deviations in $L_2$-norm for Gaussian dependent sequences (joint with S.Y. Hong and A.I. Nazarov). Electronic Comm. Probab., 2016, no. 41, 1--9.

Small deviations of smooth stationary Gaussian processes (joint with F.Aurzada, I.Ibragimov and H. van Zanten). Theory Probab. Appl., 2008, 53 788-798 (in Russian), 2009, 53, 697-707 (in English).

Abstract      Full arXiv version   Article in the journal 


Small deviations of stable processes and entropy of associated random operators (joint with F.Aurzada and W.Linde). Bernoulli, 2009, 15, no 4, 1305-1334.

Abstract    Full arXiv version    Article in the journal


On the small deviation problem for some iterated processes (joint with F.Aurzada).
Electron. J. Probab., 2009, 14, no. 68, 1992-2010.

Abstract    Full arXiv version     Article in the journal


Small deviation probability via chaining (joint with F.Aurzada). Stoch. Proc. Appl., 2008, 118, 2344-2368.

Abstract   Full arXiv  version     Article in the journal


Small deviations of Riemann-Liouville processes in L_q-norms with respect to fractal measures (joint with W. Linde and Z.Shi). Proc. London Math. Soc., 2006, 92, 224-250.

Abstract     Article in the journal

Small deviations of Gaussian random fields in L_q-spaces (joint with W. Linde and Z.Shi). Electronic J. Probab., 2006, 11, 1204-1223. 

Abstract   Full arXiv version      Article in the journal   

Probabilities of randomly centered small balls and quantization in Banach spaces (joint with S.Dereich). Ann. Probab., 2005, 33, 1397-1421.

Abstract   Full arXiv version    Article in the journal

Small deviations of weighted fractional processes and average non-linear approximation (joint with W.Linde). Trans. Amer. Math. Soc., 2005, 357, 2059-2079.

Abstract    Article in the journal


Small deviations for fractional stable processes (joint with Th.Simon). Ann. Inst. H.Poincaré, 2005, 41, 725-752.

Abstract    Full arXiv version  


Approximation and entropy numbers of Volterra operators with application to Brownian Motion (joint with W.Linde). Memoirs of Amer. Math. Soc., 2002, 157, No 745, 1-87.

Abstract

Announcement in the Notices of AMS

Item in the AMS bookstore


Probabilities of hitting of shifted small balls by centered Poisson processes (joint with P.Deheuvels), Zapiski Seminarov POMI, 2001, 278, 63-85. (in Russian) J. Math. Sci., 2003, 118 (6), 5541-5554 (in English).

Abstract   Full text (Russian)   Full text (English)


Metric entropy of integration operator and small ball probabilities of Brownian sheet (joint with T. Dunker, T. Kuhn, and W. Linde). Comptes Rendus Acad. Sci. Paris, Ser I, 1998, 326, 347-352; Journal of Approximation Theory, 1999, 101, 63-77.

Abstract    Article in JAT


Asymptotic behavior of small ball probabilities. Probab. Theory and Math. Statist. Proc. VII International Vilnius Conference (1998). VSP/TEV, 1999, 453-468.

Abstract


Small deviations of sums of independent variables (joint with T. Dunker, W. Linde). Proc. Conf. High Dimensional Probability; Ser. Progress in Probability, v.43, Birkhäuser, 1998, 59-74.

Abstract

On the lower tail probabilities of some random series, Ann. Probab., 1997, 25, 424-442.

Abstract  Article in the journal


Small deviations of Gaussian field (joint with B.S. Tsirelson). Th. Probab. Appl., 1986, 31, 557-558.

Abstract   Report in the journal


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