Exponential decay of correlation for the Stochastic Process associated to the Entropy Penalized Method
| dc.creator | Gomes, Diogo A. | |
| dc.creator | Lopes, Artur O. | |
| dc.date | 2007-04-25 | |
| dc.date.accessioned | 2026-07-07T07:58:14Z | |
| dc.date.available | 2026-07-07T07:58:14Z | |
| dc.description | In this paper we present an upper bound for the decay of correlation for the stationary stochastic process associated with the Entropy Penalized Method. Let $L(x, v):\Tt^n\times\Rr^n\to \Rr$ be a Lagrangian of the form L(x,v) = {1/2}|v|^2 - U(x) + < P, v>. For each value of $ε$ and $h$, consider the operator \Gg[ϕ](x):= -εh {ln}[\int_{\re^N} e ^{-\frac{hL(x,v)+ϕ(x+hv)}{εh}}dv], as well as the reversed operator \bar \Gg[ϕ](x):= -εh {ln}[\int_{\re^N} e^{-\frac{hL(x+hv,-v)+ϕ(x+hv)}{εh}}dv], both acting on continuous functions $ϕ:\Tt^n\to \Rr$. Denote by $ϕ_{ε,h} $ the solution of $\Gg[ϕ_{ε,h}]=ϕ_{ε,h}+λ_{ε,h}$, and by $\bar ϕ_{ε,h} $ the solution of $\bar \Gg[ϕ_{ε,h}]=\bar ϕ_{ε,h}+λ_{ε,h}$. In order to analyze the decay of correlation for this process we show that the operator $ {\cal L} (ϕ) (x) = \int e^{- \frac{h L (x,v)}ε} ϕ(x+h v) d v,$ has a maximal eigenvalue isolated from the rest of the spectrum. | |
| dc.identifier | https://arxiv.org/abs/0704.3393 | |
| dc.identifier | http://arxiv.org/abs/0704.3393 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127931 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37A25; 37N05 | |
| dc.title | Exponential decay of correlation for the Stochastic Process associated to the Entropy Penalized Method | |
| dc.type | text |