论文标题
非本地皮尔逊扩散
Non-Local Pearson diffusions
论文作者
论文摘要
在本文中，我们着重于由伯恩斯坦功能引起的非本地衍生物的某些热溶液以及由发电机或Pearson扩散的Fokker-Planck操作员给出的椭圆运算符引起的。这种非本地方程自然出现在异质培养基中粒子运动的治疗中。特别是，我们使用光谱分解结果进行通常的皮尔森扩散来利用上述方程的明确解。此外，我们提供了这种解决方案的随机表示，以随着时间变化的皮尔逊扩散。最后，我们利用这些过程的一些进一步属性，例如极限分布和长/短距离依赖性。
In this paper we focus on strong solutions of some heat-like problems with a non-local derivative in time induced by a Bernstein function and an elliptic operator given by the generator or the Fokker-Planck operator of a Pearson diffusion. Such kind of non-local equations naturally arise in the treatment of particle motion in heterogeneous media. In particular, we use spectral decomposition results for the usual Pearson diffusion to exploit explicit solutions of the aforementioned equations. Moreover, we provide stochastic representation of such solutions in terms of time-changed Pearson diffusions. Finally, we exploit some further properties of these processes, such as limit distributions and long/short-range dependence.
