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.

中文翻译：

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非本地可解决的出生-死亡过程

在本文中，我们研究了一些非局部差分-微分方程的强解，这些方程与一类出生-死亡过程联系在一起，这是通过正交多项式和某些非本征函数的本征函数的谱分解来作为皮尔逊扩散的离散近似而产生的。本地衍生产品。此外，我们根据时变的生死过程给出了这种解决方案的随机表示，并研究了它们的不变性和极限分布。最后，我们描述了上述时变的出生-死亡过程的相关结构。