small deviations, small ball probabilities, Gaussian processes.
UDC:
519.2, 519
Subject:
Small deviations for Gaussian random functions under Hilbert norm.
Main publications:
A. I. Nazarov, R. S. Pusev, “Tochnaya asimptotika malykh uklonenii v $L_2$-norme s vesom dlya nekotorykh gaussovskikh protsessov”, Veroyatnost i statistika. 14–2, Zap. nauchn. sem. POMI, 364, POMI, SPb., 2009, 166–199; J. Math. Sci. (N. Y.), 163:4 (2010), 409–429
R. S. Pusev, “Asimptotika malykh uklonenii v vesovoi kvadratichnoi norme dlya polei i protsessov Materna”, TVP, 55:1 (2010), 187–195; Theory Probab. Appl., 55:1 (2011), 164–172
R. S. Pusev, “Asimptotika malykh uklonenii protsessov Bogolyubova v kvadratichnoi norme”, TMF, 165:1 (2010), 134–144; Theoret. and Math. Phys., 165:1 (2010), 1348–1357
Ya. Yu. Nikitin, R. S. Pusev, “Tochnaya asimptotika malykh uklonenii dlya ryada brounovskikh funktsionalov”, TVP, 57:1 (2012), 98–123
A. I. Nazarov, R. S. Pusev, “Teoremy sravneniya dlya veroyatnostei malykh uklonenii vesovykh $L_2$-norm grinovskikh gaussovskikh protsessov”, Algebra i analiz, 25:3 (2013), 131–146
Ruslan Pusev, “Comparison theorems for small deviations of Green Gaussian processes in weighted $L_2$-norms”, ISSPSM`2014 and APTR+MS`2014. Book of abstracts (Trondheim, 16–21 June 2014), Institute of Informatics Problems, RAS, Moscow, 2014, 93
2.
A. I. Nazarov, R. S. Pusev, “Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms”, St. Petersburg Math. J., 25:3 (2014), 455–466
3.
A. Nazarov, R. Pusev, “The Wenbo Li comparison principle and its elaboration”, Abstracts of Russian-Chinese Seminar on Asymptotic Methods in Probability Theory and Mathematical Statistics (St. Petersburg, 10–14 June, 2013), Euler International Mathematical Institute, 2013, 28
4.
Ya. Yu. Nikitin, R. S. Pusev, “The exact asymptotic of small deviations for a series of Brownian functionals”, Theory Probab. Appl., 57:1 (2013), 60–81
5.
A. Nazarov, Ya. Nikitin, R. Pusev, “$L_2$-small ball probabilities for Gaussian processes: exact asymptotics”, Abstracts of 8th World Congress on Probability and Statistics (Istanbul), -, 2012, 267
6.
Alexander I. Nazarov, Ruslan S. Pusev, Comparison theorems for the small ball probabilities of Gaussian processes in weighted $L_2$-norms, 2012 , 10 pp., arXiv: 1211.2344
7.
Yakov Nikitin, Ruslan Pusev, “Small deviation probabilities for Brownian functionals”, ISSPSM`2011 and APTR+MS`2011. Book of abstracts (Svetlogorsk, 10–16 October 2011), Institute of Informatics Problems, RAS, Moscow, 2011, 40–41
8.
Ya. Yu. Nikitin, R. S. Pusev, “Small deviations of Brownian functionals: exact asymptotics”, Abstracts of V International Conference “Limit Theorems in Probability Theory and Their Applications” (Novosibirsk, August 15–21, 2011), Sobolev Institute of Mathematics, Novosibirsk, 2011, 35–36
9.
R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, Theoret. and Math. Phys., 165:1 (2010), 1348–1357
10.
R. S. Pusev, “Small deviation asymptotics for Matern processes and fields under weighted quadratic norm”, Theory Probab. Appl., 55:1 (2011), 164–172
11.
R. S. Pusev, Asimptotika veroyatnostei malykh uklonenii gaussovskikh protsessov v gilbertovoi norme, Diss. … kand. fiz.-matem. nauk, SPbGU, Sankt-Peterburg, 2010 , 101 pp.
12.
R. Pusev, “Small deviations for the Bogoliubov process”, 10th International Vilnius Conference on Probability Theory and Mathematical Statistics. Abstracts of Communication. (Vilnius, 28th June – 2nd July, 2010), TEV Publishers, Vilnius, 2010, 241–242
13.
A. I. Nazarov, R. S. Pusev, “Exact small deviation asymptotics in $L_2$-norm for some weighted Gaussian processes”, J. Math. Sci. (N. Y.), 163:4 (2010), 409–429
14.
R. S. Pusev, “Asimptotika malykh uklonenii protsessov Materna v $L_2$-norme s vesom”, Obozrenie prikladnoi i promyshlennoi matematiki, 16:2 (2009), 271
15.
Ya. Yu. Nikitin, R. S. Pusev, “Small deviation probabilities for Matérn processes under weighted $L_2$-norm.”, SPA 2009, Abstract book of 33rd Conference on Stochastic Processes and Their Applications (Berlin, 27th July – 31st July, 2009), Berlin, 2009, 185–186
16.
R. S. Pusev, “Small deviations for Matérn random fields and processes in the Hilbert norm”, Doklady Mathematics, 78:2 (2008), 778–780
17.
A. I. Nazarov, Ya. Yu. Nikitin, R. S. Pusev, “Small deviations of Gaussian processes in $L_2$-norm: exact asymptotics”, Transactions of the XXVI International Seminar on Stability Problems for Stochastic Models (Nahariya, Israel, October 22–26, 2007), Ort Braude College, Karmiel, Israel, 2007, 153–156
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