论文标题
非本地可解决的出生死亡过程
Non-Local Solvable Birth-Death Processes
论文作者
论文摘要
在本文中，我们研究了一些非本地差异差异方程的强溶液，这些方程与某些非局部衍生物的正交多发函数和特征函数有关，这些方程与某些非局部性衍生物的特征性分解相关的一类出生死亡过程。此外，我们在时间变化的出生死亡过程中对此类解决方案进行了随机表示，并研究了它们的不变及其极限分布。最后，我们描述了上述时间变化的出生死亡过程的相关结构。
In this paper we study strong solutions of some non-local difference-differential equations linked to a class of birth-death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth-death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth-death processes.
