Some quenched and annealed limit theorems of superprocesses in random environments
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911912548106240 |
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| author | Fan, Zeteng Hong, Jieliang Xiong, Jie |
| author_facet | Fan, Zeteng Hong, Jieliang Xiong, Jie |
| contents | Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W=\{W(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. When $d\geq 3$, under the condition that the correlation function $g(x,y)$ is bounded above by some appropriate function $\bar{g}(x-y)$, we present the quenched and annealed Strong Law of Large Numbers and the Central Limit Theorems regarding the weighted occupation measure $\int_0^t X_s ds$ as $t\to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some quenched and annealed limit theorems of superprocesses in random environments Fan, Zeteng Hong, Jieliang Xiong, Jie Probability 60H15, 60G57, 60J80 Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W=\{W(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. When $d\geq 3$, under the condition that the correlation function $g(x,y)$ is bounded above by some appropriate function $\bar{g}(x-y)$, we present the quenched and annealed Strong Law of Large Numbers and the Central Limit Theorems regarding the weighted occupation measure $\int_0^t X_s ds$ as $t\to \infty$. |
| title | Some quenched and annealed limit theorems of superprocesses in random environments |
| topic | Probability 60H15, 60G57, 60J80 |
| url | https://arxiv.org/abs/2406.06905 |