论文标题
组件和两个或多个$ p $ - adiC尺寸的布朗运动的退出时间
Components and Exit Times of Brownian Motion in two or more $p$-Adic Dimensions
论文作者
论文摘要
$ d $ fold产品在$ p $ - addic数字的$ d $ fold产品上定义的伪分别方程的基本解决方案，$ \ mathbb {q} _p $，在$ \ mathbb {q} _p} _p^d $中诱导Wiener流程的类似物。就像在实际环境中一样，组件为$ 1 $二维$ p $ - adic的布朗尼运动，其扩散常数和指数与原始过程相同。条件概率的渐近分析表明，载体成分一直依赖。较高维度过程的退出时间概率揭示了组件依赖性的具体效应。
The fundamental solution of a pseudo-differential equation for functions defined on the $d$-fold product of the $p$-adic numbers, $\mathbb{Q}_p$, induces an analogue of the Wiener process in $\mathbb{Q}_p^d$. As in the real setting, the components are $1$-dimensional $p$-adic Brownian motions with the same diffusion constant and exponent as the original process. Asymptotic analysis of the conditional probabilities shows that the vector components are dependent for all time. Exit time probabilities for the higher dimensional processes reveal a concrete effect of the component dependency.
