On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape
| Autor: | Castro, Matheus M., Goverse, Vincent P. H., Lamb, Jeroen S. W., Rasmussen, Martin |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/etds.2023.69 |
| Popis: | In this paper, we consider absorbing Markov chains $X_n$ admitting a quasi-stationary measure $\mu$ on $M$ where the transition kernel $\mathcal P$ admits an eigenfunction $0\leq \eta\in L^1(M,\mu)$. We find conditions on the transition densities of $\mathcal P$ with respect to $\mu$ which ensure that $\eta(x) \mu(\mathrm d x)$ is a quasi-ergodic measure for $X_n$ and that the Yaglom limit converges to the quasi-stationary measure $\mu$-almost surely. We apply this result to the random logistic map $X_{n+1} = \omega_n X_n (1-X_n)$ absorbed at $\mathbb R \setminus [0,1],$ where $\omega_n$ is an i.i.d sequence of random variables uniformly distributed in $[a,b],$ for $1\leq a <4$ and $b>4.$ Comment: 35 pages, 0 figures |
| Databáze: | arXiv |
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