VARIATIONAL FORMULATION OF THE FOKKER–PLANCK EQUATION WITH DECAY: A PARTICLE APPROACH
VARIATIONAL FORMULATION OF THE FOKKER–PLANCK EQUATION WITH DECAY: A PARTICLE APPROACH
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带有衰变的福克-普朗克方程的变分公式：粒子方法
DOI：
10.1142/s021919971350017x
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发表时间：
2011
影响因子：
1.6
通讯作者：
Marco Veneroni
中科院分区：
文献类型：
--
作者：
M. Peletier;M. Renger;Marco Veneroni
我们引入了一个对应于多粒子极限衰减的福克-普朗克方程的随机粒子系统，并研究了它的大偏差。我们证明大偏差率泛函对应于 Mosco 收敛意义上的能量耗散泛函。此外，我们证明所得到的泛函（涉及熵项和 Wasserstein 度量）再次是带有衰减的 Fokker-Planck 方程的变分公式。
We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is again a variational formulation for the Fokker–Planck equation with decay.