论文标题
锥体中的多结功能和随机过程
Polyharmonic functions and random processes in cones
论文作者
论文摘要
我们研究了与布朗运动和随机行走有关的多结功能。这些功能可以在连续的环境和离散设置中取消通常的Laplacian的某些功能。我们表明，在考虑布朗案中热核的渐近膨胀以及在格朗案中的渐进式枚举问题中，多谐功能自然出现。我们提供了一种通过拉普拉斯转换和在连续和离散的情况下产生函数来构建一般多结的函数的方法。这是通过使用功能方程方法来完成的。
We investigate polyharmonic functions associated to Brownian motion and random walks in cones. These are functions which cancel some power of the usual Laplacian in the continuous setting and of the discrete Laplacian in the discrete setting. We show that polyharmonic functions naturally appear while considering asymptotic expansions of the heat kernel in the Brownian case and in lattice walk enumeration problems. We provide a method to construct general polyharmonic functions through Laplace transforms and generating functions in the continuous and discrete cases, respectively. This is done by using a functional equation approach.
