For each prime p, a diffusion constant together with a positive exponent specify a Vladimirov operator and an associated p-adic diffusion equation. The fundamental solution of this pseudo-differential equation gives rise to a measure on the Skorokhod space of p-adic valued paths that is concentrated on the paths originating at the origin. We calculate the first exit probabilities of paths from balls and estimate these probabilities for the Brownian bridges.

中文翻译：

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p -Adic Brownian桥的某些出口概率的估计

对于每个素数p，扩散常数与正指数一起指定Vladimirov算子和相关的p -adic扩散方程。该伪微分方程的基本解引起对p -adic值路径的Skorokhod空间的度量，该度量集中在始于原点的路径上。我们计算球的路径的第一个出口概率，并估计布朗桥的这些概率。