Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment
For a continuous-time lattice random walk $X^\Lambda=\set{X^\Lambda_t,t\ge 0}$ in a random environment $\Lambda$, we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X^\Lambda_s)ds$, $t\ge 0$. We establish a limit theorem for it, which...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2023-08-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1758 |
| _version_ | 1827859091530186752 |
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| author | Georgiy Shevchenko Andrii Yaroshevskiy |
| author_facet | Georgiy Shevchenko Andrii Yaroshevskiy |
| author_sort | Georgiy Shevchenko |
| collection | DOAJ |
| description |
For a continuous-time lattice random walk $X^\Lambda=\set{X^\Lambda_t,t\ge 0}$ in a random environment $\Lambda$, we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X^\Lambda_s)ds$, $t\ge 0$. We establish a limit theorem for it, which is similar to that in the non-lattice case, under less restrictive assumptions.
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| first_indexed | 2024-03-12T13:03:24Z |
| format | Article |
| id | doaj.art-5dc721dfaba64a19ae7e1163934663c9 |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-03-12T13:03:24Z |
| publishDate | 2023-08-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-5dc721dfaba64a19ae7e1163934663c92023-08-28T18:34:36ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2023-08-0152SI10.17713/ajs.v52iSI.1758Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random EnvironmentGeorgiy ShevchenkoAndrii Yaroshevskiy For a continuous-time lattice random walk $X^\Lambda=\set{X^\Lambda_t,t\ge 0}$ in a random environment $\Lambda$, we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X^\Lambda_s)ds$, $t\ge 0$. We establish a limit theorem for it, which is similar to that in the non-lattice case, under less restrictive assumptions. https://www.ajs.or.at/index.php/ajs/article/view/1758 |
| spellingShingle | Georgiy Shevchenko Andrii Yaroshevskiy Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment Austrian Journal of Statistics |
| title | Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment |
| title_full | Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment |
| title_fullStr | Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment |
| title_full_unstemmed | Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment |
| title_short | Limit Theorems for Additive Functionals of Continuous-Time Lattice Random Walks in a Stationary Random Environment |
| title_sort | limit theorems for additive functionals of continuous time lattice random walks in a stationary random environment |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1758 |
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