论文标题
与Jacobi-Koornwinder双变量多项式相关的QBD过程
QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models
论文作者
论文摘要
我们研究了与所谓的Jacobi-koornwinder双变量多项式的第一家族相关的准生物和死亡（QBD）的家族。这些多项式在通常被称为燕尾的边界区域上是正交的。我们将显式计算这些QBD多项式产生的三项复发关系的系数，并研究我们可以产生离散时间QBD过程家族的条件。最后，我们显示了与这些QBD过程的一种特殊情况相关的urn模型。
We study a family of quasi-birth-and-death (QBD) processes associated with the so-called first family of Jacobi-Koornwinder bivariate polynomials. These polynomials are orthogonal on a bounded region typically known as the swallow tail. We will explicitly compute the coefficients of the three-term recurrence relations generated by these QBD polynomials and study the conditions under we can produce families of discrete-time QBD processes. Finally, we show an urn model associated with one special case of these QBD processes.
