کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8954739 | 1646042 | 2018 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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 (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 Markov 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 divergence, thus also in the total variation norm. The results show that there is a relation between the Bakry-Ãmery 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 128, Issue 10, October 2018, Pages 3253-3272
Journal: Stochastic Processes and their Applications - Volume 128, Issue 10, October 2018, Pages 3253-3272
نویسندگان
Luu Hoang Duc, Tat Dat Tran, Jürgen Jost,