论文标题
渐近行为，用于时间均匀的kolmogorov型扩散
Asymptotic behaviour for a time-inhomogeneous Kolmogorov type diffusion
论文作者
论文摘要
我们研究了具有非线性时间抗性阻力和布朗型随机力的动力学随机模型。更确切地说，考虑到Kolmogorov类型扩散$（V，X）$：这里$ x $是粒子的位置，$ v $是其速度，是解决由一维的布朗尼运动驱动的随机微分方程的方法，由一维的布朗运动驱动，形式$ t^{ - β} f（v（v）$。功能$ f $满足某些同质性条件，$β$是正的。通过使用随机分析工具证明了过程$（v，x）$的行为。
We study a kinetic stochastic model with a non-linear time-inhomogeneous drag force and a Brownian-type random force. More precisely, the Kolmogorov type diffusion $(V,X)$ is considered: here $X$ is the position of the particle and $V$ is its velocity and is solution of a stochastic differential equation driven by a one-dimensional Brownian motion, with the drift of the form $t^{-β}F(v)$. The function $F$ satisfies some homogeneity condition and $β$ is positive. The behaviour of the process $(V,X)$ in large time is proved by using stochastic analysis tools.
