论文标题
非XtaniveItô-Langevin动力学
Nonextensive Itô-Langevin Dynamics
论文作者
论文摘要
我们研究了非xty恒温量一致的ITô-Langevin动力学的概括。相应的随机微分方程与描述分形相关的异常扩散的一类广泛的非线性fokker-planck方程相连。提出了广义的中央限制定理，以证明该方程如何作为相关随机变量的极限出现。在此过程中，我们将相关异常扩散的显微镜和宏观描述以数学上的声音方式连接起来，并解释了为什么$ q $ -Gaussian分布在本质上经常出现。
We study generalizations of Itô-Langevin dynamics consistent within nonextensive thermostatistics. The corresponding stochastic differential equations are shown to be connected with a wide class of nonlinear Fokker-Planck equations describing correlated anomalous diffusion in fractals. A generalized central limit theorem is proposed in order to demonstrate how such equations emerge as a limit of correlated random variables. In doing so, we connect microscopic and macroscopic descriptions of correlated anomalous diffusion in a mathematically sound way and shed some light in explaining why $q$-Gaussian distributions appear quite often in nature.
