Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

Authors:

Chii-Ruey Hwang Shuenn-Jyi Sheu

Institution:

1. Institute of Mathematics, Academia Sinica, 11529, Taipei, Taiwan

Abstract:

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + epsi

(X (t)) dB(t). A crucial constant Lambda

appears naturally in our study. Heuristically, when the time is of the order exp( Lambda

–

² , the transition density has a good lower bound and when the process has run for about exp( Lambda

–

², it is very close to the invariant measure. LetL =( epsi

²/2)

–

U ·

be a second-order differential operator on Ropf

^d. Under suitable conditions,L ^z has the discrete spectrum

$\begin{gathered} 0 = \lambda _1^\varepsilon > - \lambda _2^\varepsilon ...and lim \varepsilon ^2 log \lambda _2^\varepsilon = - \Lambda \hfill \\ \varepsilon \to 0 \hfill \\ \end{gathered}$

Keywords:	AMS subject classifications (1980)" target="_blank">AMS subject classifications (1980) Primary 60H10 60J70 secondary 60F10 35P15
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