多分枝树叶子上的跳过程
Jump processes on leaves of multibranching trees
摘要：
p-adic数已经在广泛的不同研究领域中找到了应用。在某些应用中，p-代数的代数性质成为理论中不可缺少的组成部分。另一类应用程序与层次树系统有关。在这种情况下，应用程序是基于众所周知的对应关系p-adics和树与p-分支出现从每个分支点。然后代数结构不进入和p-adics仅用作标记系统的树枝。我们引入了一个空间的数字序列适合于标记的树与不同数量的分支出现的分支点。我们给这个空间赋予了一个非阿基米德度量，并描述了它的基本拓扑性质。我们还表明，已知的建设的随机过程的p-adics进行上述空间上的随机过程，因此在相应的树。
英文摘要：
The p-adic numbers have found applications in a wide range of diverse fields of research. In some applications the algebraic properties of p-adics enter as an indispensable ingredient of the theory. Another class of applications has to do with hierarchical tree like systems. In this context the applications are based on the well known correspondence between p-adics and the trees with p-branches emerging from every branching point. Then the algebraic structure does not enter and p-adics are used merely as a labeling system for the tree branches. We introduce a space of numerical sequences suitable for labeling the trees with varying number of branches emerging from the branching points. We equipe this space with a non Archimedian metric and describe its basic topological properties. We also demonstrate that the known construction of the stochastic processes on p-adics carry over to the stochastic processes on the above mentioned space and hence on the corresponding trees.
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