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- W4301490816 abstract "It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada-Watanabe theorem cite{yamada1,yamada2} and the Feller test for explosions cite{feller51,feller54}, there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called {it 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 {divergence}, thus also in the total variation norm. The results show that there is a relation between the Bakry-Emery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher-Lamperti transformation. Several applications are discussed, including the Cox-Ingersoll-Ross model and the Ait-Sahalia model in finance and the Wright-Fisher model in population genetics." @default.
- W4301490816 created "2022-10-05" @default.
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- W4301490816 date "2016-08-24" @default.
- W4301490816 modified "2023-09-26" @default.
- W4301490816 title "Ergodicity of scalar stochastic differential equations with Holder continuous coefficients" @default.
- W4301490816 doi "https://doi.org/10.48550/arxiv.1608.06785" @default.
- W4301490816 hasPublicationYear "2016" @default.
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