Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation
The paper deals with a stochastic heat equation driven by an additive fractional Brownian space-only noise. We prove that a solution to this equation is a stationary and ergodic Gaussian process. These results enable us to construct a strongly consistent estimator of the diffusion parameter.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2020-09-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/20-VMSTA162 |
| _version_ | 1818113823787188224 |
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| author | Diana Avetisian Kostiantyn Ralchenko |
| author_facet | Diana Avetisian Kostiantyn Ralchenko |
| author_sort | Diana Avetisian |
| collection | DOAJ |
| description | The paper deals with a stochastic heat equation driven by an additive fractional Brownian space-only noise. We prove that a solution to this equation is a stationary and ergodic Gaussian process. These results enable us to construct a strongly consistent estimator of the diffusion parameter. |
| first_indexed | 2024-12-11T03:40:58Z |
| format | Article |
| id | doaj.art-c7cbb78ee1fd4c6185242452f73322ec |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-11T03:40:58Z |
| publishDate | 2020-09-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-c7cbb78ee1fd4c6185242452f73322ec2022-12-22T01:22:08ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542020-09-017333935610.15559/20-VMSTA162Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimationDiana Avetisian0Kostiantyn Ralchenko1Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601 Kyiv, UkraineDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601 Kyiv, UkraineThe paper deals with a stochastic heat equation driven by an additive fractional Brownian space-only noise. We prove that a solution to this equation is a stationary and ergodic Gaussian process. These results enable us to construct a strongly consistent estimator of the diffusion parameter.https://www.vmsta.org/doi/10.15559/20-VMSTA162Stochastic partial differential equationfractional Brownian motionstationary processergodic processstrong consistency |
| spellingShingle | Diana Avetisian Kostiantyn Ralchenko Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation Modern Stochastics: Theory and Applications Stochastic partial differential equation fractional Brownian motion stationary process ergodic process strong consistency |
| title | Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation |
| title_full | Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation |
| title_fullStr | Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation |
| title_full_unstemmed | Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation |
| title_short | Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation |
| title_sort | ergodic properties of the solution to a fractional stochastic heat equation with an application to diffusion parameter estimation |
| topic | Stochastic partial differential equation fractional Brownian motion stationary process ergodic process strong consistency |
| url | https://www.vmsta.org/doi/10.15559/20-VMSTA162 |
| work_keys_str_mv | AT dianaavetisian ergodicpropertiesofthesolutiontoafractionalstochasticheatequationwithanapplicationtodiffusionparameterestimation AT kostiantynralchenko ergodicpropertiesofthesolutiontoafractionalstochasticheatequationwithanapplicationtodiffusionparameterestimation |