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2013 | 11 | 12 | 2089-2098
Tytuł artykułu

Small deviations of iterated processes in the space of trajectories

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
12
Strony
2089-2098
Opis fizyczny
Daty
wydano
2013-12-01
online
2013-10-08
Twórcy
Bibliografia
  • [1] Aurzada F., Lifshits M., On the small deviation problem for some iterated processes, Electron. J. Probab., 2009, 14,#68, 1992–2010
  • [2] Baumgarten C., Survival probabilities of some iterated processes, preprint available at http://arxiv.org/abs/1106.2999
  • [3] Borovkov A.A., Mogul’skii A.A., On probabilities of small deviations for stochastic processes, Siberian Adv. Math., 1991, 1(1), 39–63
  • [4] Fatalov V.R., Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields, Russian Math. Surveys, 2003, 58(4), 725–772 http://dx.doi.org/10.1070/RM2003v058n04ABEH000643
  • [5] Frolov A.N., On probabilities of small deviations for compound Cox processes, J. Math. Sci. (N.Y.), 2007, 145(2), 4931–4937 http://dx.doi.org/10.1007/s10958-007-0327-7
  • [6] Frolov A.N., On asymptotic behaviour of probabilities of small deviations for compound Cox processes, Theory Stoch. Process., 2008, 14(2), 19–27
  • [7] Frolov A.N., Limit theorems for small deviation probabilities of some iterated stochastic processes, J. Math. Sci. (N.Y.), 2013, 188(6), 761–768 http://dx.doi.org/10.1007/s10958-013-1169-0
  • [8] Ledoux M., Isoperimetry and Gaussian analysis, In: Lectures on Probability Theory and Statistics, Saint-Flour, July 7–23, 1994, Lecture Notes in Math., 1648, Springer, Berlin, 1996, 165–294
  • [9] Li W.V., Shao Q.-M., Gaussian processes: inequalities, small ball probabilities and applications, In: Stochastic Processes: Theory and Methods, Handbook of Statist., 19, North-Holland, Amsterdam, 2001, 533–597 http://dx.doi.org/10.1016/S0169-7161(01)19019-X
  • [10] Li W. V., Shao Q.-M., Recent developments on lower tail probabilities for Gaussian processes, Cosmos, 2005, 1(1), 95–106 http://dx.doi.org/10.1142/S0219607705000103
  • [11] Lifshits M.A., Asymptotic behavior of small ball probabilities, In: Proceedings of the Seventh Vilnius Conference on Probability Theory and Mathematical Statistics, VSP/TEV. Vilnius, 1999, 453–468
  • [12] Lifshits M.A., Bibliography of small deviation probabilities, available at http://www.proba.jussieu.fr/pageperso/smalldev/biblio.pdf
  • [13] Martikainen A.I., Frolov A.N., Steinebach J., On probabilities of small deviations for compound renewal processes, Theory Probab. Appl., 2007, 52(2), 328–337
  • [14] Mogul’skii A.A., Small deviations in a space of trajectories, Theory Probab. Appl., 1974, 19(4), 726–736 http://dx.doi.org/10.1137/1119081
  • [15] Nane E., Laws of the iterated logarithm for α-time Brownian motion, Electron. J. Probab., 2006, 11(18), 434–459
  • [16] Nane E., Laws of the iterated logarithm for a class of iterated processes, Statist. Probab. Lett., 2009, 79(16), 1744–1751 http://dx.doi.org/10.1016/j.spl.2009.04.013
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0316-7
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