Convergence in distribution of some particular self-interacting diffusions: the simulated annealing method
| dc.creator | Chambeu, Sebastien | |
| dc.creator | Kurtzmann, Aline | |
| dc.date | 2007-07-19 | |
| dc.date | 2008-12-04 | |
| dc.date.accessioned | 2026-07-07T12:08:55Z | |
| dc.date.available | 2026-07-07T12:08:55Z | |
| dc.description | The present paper is concerned with some self-interacting diffusions $(X_t,t\geq 0)$ living on $\mathbb{R}^d$. These diffusions are solutions to stochastic differential equations: $$\mathrm{d}X_t = \mathrm{d}B_t - g(t)\nabla V(X_t - \barμ_t) \mathrm{d}t$$ where $\barμ_t$ is the empirical mean of the process $X$, $V$ is an asymptotically strictly convex potential and $g$ is a given function. The authors have still studied the ergodic behavior of $X$ and proved that it is strongly related to $g$. We go further and give necessary and sufficient conditions (for small $g$'s) in order that $X$ converges in probability to $X_\infty$ (which is related to the global minima of $V$). | |
| dc.description | companion paper to 0707.2908 | |
| dc.identifier | https://arxiv.org/abs/0707.2910 | |
| dc.identifier | http://arxiv.org/abs/0707.2910 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209460 | |
| dc.subject | Probability | |
| dc.title | Convergence in distribution of some particular self-interacting diffusions: the simulated annealing method | |
| dc.type | text |