Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 

 

Stochastic processes in the spaces $ D_{V,W}$


Authors: Yu. V. Kozachenko and O. M. Moklyachuk
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal: Theor. Probability and Math. Statist. 82 (2011), 43-56
MSC (2010): Primary 60G07
DOI: https://doi.org/10.1090/S0094-9000-2011-00826-5
Published electronically: August 2, 2011
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the spaces of random variables $ D_{V,W}$. We study the conditions for the convergence of series and the distribution of the supremum of stochastic processes in these spaces.


References [Enhancements On Off] (What's this?)

  • 1. V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
  • 2. Yu. V. Kozachenko, On the distribution of the supremum of random processes in quasi-Banach 𝐾_{𝜎}-spaces, Ukraïn. Mat. Zh. 51 (1999), no. 7, 918–930 (Ukrainian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 51 (1999), no. 7, 1029–1043 (2000). MR 1727696, https://doi.org/10.1007/BF02592039
  • 3. V. V. Buldygin, \cyr Skhodimost′ sluchaĭnykh èlementov v topologicheskikh prostranstvakh, “Naukova Dumka”, Kiev, 1980 (Russian). MR 734899
  • 4. E. A. Abzhanov and Yu. V. Kozachenko, Some properties of random processes in Banach 𝐾_{𝜎}-spaces, Ukrain. Mat. Zh. 37 (1985), no. 3, 275–280, 403 (Russian). MR 795565
  • 5. E. A. Abzhanov and Yu. V. Kozachenko, Random processes in quasi-Banach 𝐾_{𝜎}-spaces of random variables, Probabilistic methods for the investigation of systems with an infinite number of degrees of freedom (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1986, pp. 4–11, i (Russian). MR 895373
  • 6. Yu. V. Kozachenko and E. I. Ostrovskiĭ, Banach spaces of random variables of sub-Gaussian type, Teor. Veroyatnost. i Mat. Statist. 32 (1985), 42–53, 134 (Russian). MR 882158
  • 7. Yu. V. Kozachenko, Random processes in Orlicz spaces. I, Teor. Veroyatnost. i Mat. Statist. 30 (1984), 92–107, 152 (Russian). MR 800835
  • 8. Yu. V. Kozachenko, Random processes in Orlicz spaces. II, Teor. Veroyatnost. i Mat. Statist. 31 (1984), 44–50, 143 (Russian). MR 816125

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G07

Retrieve articles in all journals with MSC (2010): 60G07


Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: yvk@univ.kiev.ua

O. M. Moklyachuk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: omoklyachuk@ukr.net

DOI: https://doi.org/10.1090/S0094-9000-2011-00826-5
Keywords: Stochastic processes, prenorm, quasinorm, pre-Banach space, quasi-Banach space, the convergence of series
Received by editor(s): January 21, 2010
Published electronically: August 2, 2011
Additional Notes: The first author is grateful to the Department of Mathematics and Statistics of the University “La Trobe”, Melbourne, for support in the framework of the research grant “Stochastic Approximation in Finance and Signal Processing”
Article copyright: © Copyright 2011 American Mathematical Society