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原文連結
論文資訊
- 類型：已發表論文
- 日期：2017-11-08
摘要
It is well-known that for a one dimensional 隨機 differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada-Watanabe theorem (Yamada and Watanabe, 1971, [31,32]) and the Feller test for explosions (Feller, 1951, 1954), there exists a unique stationary distribution with respect to the 馬可夫 semigroup of transition probabilities. We consider systems on a restricted domain D of the phase space R and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called free energy function on the density function space, we prove that the density functions, which are solutions of the Fokker-Planck equation, converge to the stationary density function exponentially under the Kullback-Leibler diverge
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