论文标题
估计通过光谱差距的F-连接的指数收敛速率
Estimate the exponential convergence rate of f-ergodicity via spectral gap
论文作者
论文摘要
本文研究了连续时间马尔可夫链的F-连续性及其指数收敛速率。假设F是正方形的，对于可逆的Markov链，证明F-连接性的指数收敛性在且仅当发电机的光谱间隙为正时。此外，收敛速率等于光谱间隙。对于不可逆转的情况，光谱差距的阳性仍然是F-连通性的足够条件。这些结果的有效性通过一些典型示例说明了。
This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, for reversible Markov chain, it is proved that the exponential convergence of f-ergodicity holds if and only if the spectral gap of the generator is positive. Moreover, the convergence rate is equal to the spectral gap. For irreversible case, the positivity of spectral gap remains a sufficient condition of f-ergodicity. The effectiveness of these results are illustrated by some typical examples.
