Sample continuity and modeling of stochastic processes from the spaces \(D_{V,W}\). (English. Russian original) Zbl 1251.60030

Kozachenko, Yu. V.; Moklyachuk, O. M.

Theory Probab. Math. Stat. 83, 95-110 (2011); translation from Teor. Jmovirn. Mat. Stat. 83, 80-91 (2010).

Random sequences and stochastic processes belonging to the space \(D_{V,W}\) are studied. The spaces \(D_{V,W}\) are defined as pre-Banach spaces generated by pre-metrics \(||\xi||=\sup\limits_{x\geq0}V(x)W^{(-1)}(P\{|\xi|>x\})\). Models of stochastic processes belonging to the space \(D_{V,W}\) are investigated. Moreover several examples of models are given.

Reviewer: Nicko G. Gamkrelidze (Moskva)

MSC:

60G07	General theory of stochastic processes
60G20	Generalized stochastic processes

Keywords:

stochastic processes; modeling of stochastic processes; pre-Banach spaces; spaces \(D_{V,W}\); pre-metrics

References:

[1]	Yu. V. Kozachenko and O. M. Moklyachuk, Random processes in the spaces \?_{\?,\?}, Teor. Ĭmovīr. Mat. Stat. 82 (2010), 56 – 66 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 82 (2011), 43 – 56. · Zbl 1232.60030 · doi:10.1090/S0094-9000-2011-00826-5
[2]	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. · Zbl 0998.60503
[3]	Yu. V. Kozachenko, On the distribution of the supremum of random processes in quasi-Banach \?_{\?}-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). · Zbl 0956.60025 · doi:10.1007/BF02592039
[4]	Сходимост\(^{\приме}\) случайных ѐлементов в топологических пространствах, ”Наукова Думка”, Киев, 1980 (Руссиан).
[5]	E. A. Abzhanov and Yu. V. Kozachenko, Some properties of random processes in Banach \?_{\?}-spaces, Ukrain. Mat. Zh. 37 (1985), no. 3, 275 – 280, 403 (Russian). · Zbl 0582.60046
[6]	E. A. Abzhanov and Yu. V. Kozachenko, Random processes in quasi-Banach \?_{\?}-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). · Zbl 0628.60052
[7]	Yu. V. Kozachenko, Random processes in Orlicz spaces. I, Teor. Veroyatnost. i Mat. Statist. 30 (1984), 92 – 107, 152 (Russian).
[8]	Yu. V. Kozachenko, Random processes in Orlicz spaces. II, Teor. Veroyatnost. i Mat. Statist. 31 (1984), 44 – 50, 143 (Russian).