论文标题
与非对称界面的简单动力学模型的扩散近似
Diffusion approximation for a simple kinetic model with asymmetric interface
论文作者
论文摘要
我们研究了一个空间维度中粒子随机运动模型的扩散近似。粒子的速度是恒定的，但是运动的方向通过泊松时钟发生随机变化。此外，粒子与界面相互作用，以使其可以随机反映，传输或杀死，并且相应的概率取决于粒子是从左侧还是右侧到达界面。我们证明，如果杀戮的概率为正，则极限过程是最小的布朗运动。在没有杀人的情况下，极限是偏斜的布朗尼运动。
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover, the particle interacts with an interface in such a way that it can randomly be reflected, transmitted, or killed, and the corresponding probabilities depend on whether the particle arrives at the interface from the left, or right. We prove that the limit process is a minimal Brownian motion, if the probability of killing is positive. In the case of no killing, the limit is a skew Brownian motion.
