Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions
In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions o...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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VTeX
2019-12-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/19-VMSTA146 |
| _version_ | 1819066444023857152 |
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| author | Yuriy Kozachenko Enzo Orsingher Lyudmyla Sakhno Olga Vasylyk |
| author_facet | Yuriy Kozachenko Enzo Orsingher Lyudmyla Sakhno Olga Vasylyk |
| author_sort | Yuriy Kozachenko |
| collection | DOAJ |
| description | In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition. |
| first_indexed | 2024-12-21T16:02:27Z |
| format | Article |
| id | doaj.art-7e95f9a884e848dd820e255aef96c6f1 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-21T16:02:27Z |
| publishDate | 2019-12-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-7e95f9a884e848dd820e255aef96c6f12022-12-21T18:57:58ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542019-12-0171799610.15559/19-VMSTA146Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditionsYuriy Kozachenko0Enzo Orsingher1Lyudmyla Sakhno2Olga Vasylyk3Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska str., 01601, Kyiv, UkraineDepartment of Statistical Sciences, Sapienza University of Rome, P.le Aldo Moro, 5, 00185, Rome, ItalyDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska str., 01601, Kyiv, UkraineDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska str., 01601, Kyiv, UkraineIn the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition.https://www.vmsta.org/doi/10.15559/19-VMSTA146Higher-order dispersive equationsrandom initial conditionsharmonizable processessub-Gaussian processesdistribution of sumpremum of solutionentropy methods |
| spellingShingle | Yuriy Kozachenko Enzo Orsingher Lyudmyla Sakhno Olga Vasylyk Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions Modern Stochastics: Theory and Applications Higher-order dispersive equations random initial conditions harmonizable processes sub-Gaussian processes distribution of sumpremum of solution entropy methods |
| title | Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions |
| title_full | Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions |
| title_fullStr | Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions |
| title_full_unstemmed | Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions |
| title_short | Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions |
| title_sort | estimates for distribution of suprema of solutions to higher order partial differential equations with random initial conditions |
| topic | Higher-order dispersive equations random initial conditions harmonizable processes sub-Gaussian processes distribution of sumpremum of solution entropy methods |
| url | https://www.vmsta.org/doi/10.15559/19-VMSTA146 |
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