Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes
This paper investigates sample paths properties of φ-sub-Gaussian processes by means of entropy methods. Basing on a particular entropy integral, we treat the questions on continuity and the rate of growth of sample paths. The obtained results are then used to investigate the sample paths properties...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2021-01-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/21-VMSTA171 |
| _version_ | 1818618696013185024 |
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| author | Olha Hopkalo Lyudmyla Sakhno |
| author_facet | Olha Hopkalo Lyudmyla Sakhno |
| author_sort | Olha Hopkalo |
| collection | DOAJ |
| description | This paper investigates sample paths properties of φ-sub-Gaussian processes by means of entropy methods. Basing on a particular entropy integral, we treat the questions on continuity and the rate of growth of sample paths. The obtained results are then used to investigate the sample paths properties for a particular class of φ-sub-Gaussian processes related to the random heat equation. We derive the estimates for the distribution of suprema of such processes and evaluate their rate of growth. |
| first_indexed | 2024-12-16T17:25:41Z |
| format | Article |
| id | doaj.art-ee95bf244fd9417096725abbe62cc01a |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-16T17:25:41Z |
| publishDate | 2021-01-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-ee95bf244fd9417096725abbe62cc01a2022-12-21T22:23:03ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542021-01-0181416210.15559/21-VMSTA171Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processesOlha Hopkalo0Lyudmyla Sakhno1Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64, Volodymyrs’ka St., 01601 Kyiv, UkraineDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64, Volodymyrs’ka St., 01601 Kyiv, UkraineThis paper investigates sample paths properties of φ-sub-Gaussian processes by means of entropy methods. Basing on a particular entropy integral, we treat the questions on continuity and the rate of growth of sample paths. The obtained results are then used to investigate the sample paths properties for a particular class of φ-sub-Gaussian processes related to the random heat equation. We derive the estimates for the distribution of suprema of such processes and evaluate their rate of growth.https://www.vmsta.org/doi/10.15559/21-VMSTA171<italic>φ</italic>-sub-Gaussian processesdistribution of sumpremumrate of growthentropy methodsHeat equationrandom initial conditions |
| spellingShingle | Olha Hopkalo Lyudmyla Sakhno Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes Modern Stochastics: Theory and Applications <italic>φ</italic>-sub-Gaussian processes distribution of sumpremum rate of growth entropy methods Heat equation random initial conditions |
| title | Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes |
| title_full | Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes |
| title_fullStr | Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes |
| title_full_unstemmed | Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes |
| title_short | Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes |
| title_sort | investigation of sample paths properties for some classes of φ sub gaussian stochastic processes |
| topic | <italic>φ</italic>-sub-Gaussian processes distribution of sumpremum rate of growth entropy methods Heat equation random initial conditions |
| url | https://www.vmsta.org/doi/10.15559/21-VMSTA171 |
| work_keys_str_mv | AT olhahopkalo investigationofsamplepathspropertiesforsomeclassesofphsubgaussianstochasticprocesses AT lyudmylasakhno investigationofsamplepathspropertiesforsomeclassesofphsubgaussianstochasticprocesses |