Theory of Probability and Mathematical Statistics
Sample Continuity conditions with probability one for Square-Gaussian Stochastic Processes
Yu. V. Kozachenko, I. V. Rozora
Download PDF
Abstract: A Square-Gaussian Stochastic Processes are considered.
Keywords:
Bibliography: ample uniform continuity conditions of such processes
with probability on the compact are found. The estimation of the
distribution for modulus continuity of Square-Gaussian process is
obtained.
Bibliography: 1. V. V. Buldygin, Yu. V. Kozachenko, Metric characterization of random variables and random processes, Amer. Math. Soc., Providence, RI, 2000.
2. R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis, 1 (1967), 290-330.
3. I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Processes, vol. 1, Naukà, Moscow, 1977. (In Russian)
4. Yu. V. Kozachenko, O. M. Moklyachuk, Large deviation probabilities for square-Gaussian stochastic processes, Extremes, 2 (1999), no. 3, 269-293.
5. Yu. V. Kozachenko, O. O. Pogorilyak, I. V. Rozora, A. M. Tegza, Simulation of Stochastic Processes with Given Accuracy and Reliability, ISTE Press - Elsevier, 2016.
6. Yu. V. Kozachenko, I. V. Rozora, A criterion for testing hypothesis about impulse response function, Stat., Optim. Inf. Comput., 4 (2016), no. 3, 214-232.
7. Yu. V. Kozachenko, O. V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Communications, 3 (1998), no. 1, 83-94.
8. A. O. Pashko, I. V. Rozora, Accuracy of simulation for the network tra c in the form of fractional Brownian Motion, 14-th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering, TCSET, Proceedings (2018), 840-845.
9. I. V. Rozora, Statistical hypothesis testing for the shape of impulse response function, Communications in Statistics - Theory and Methods, 47 (2018), no. 6, 1459-1474.
10. I. V. Rozora, M. V. Lyzhechko, On the modeling of linear system input stochastic processes with given accuracy and reliability, Monte Carlo Methods Appl., 24 (2018), no. 2, 129-137.
