论文标题
$ p $ - adic布朗运动是一个缩放限制
$p$-Adic Brownian Motion is a Scaling Limit
论文作者
论文摘要
$ p $ - adic的布朗尼运动是一个连续的时间随机过程，在$ p $ ad的状态空间中，它以弗拉基米罗夫操作员为无限发电机。当前的工作表明，任何此类过程都是离散组上离散时间随机步行的缩放限制。较早的工作要求Vladimirov Operator的指数为$（1，\ infty）$，并且收敛是在紧凑的时间间隔上skorohod空间上概率度量的弱收敛性。当前的方法简化了较早的方法，允许任何正指数，消除了紧凑时间间隔的限制，并为具有独立关注的离散时间过程确定了一些力矩估计。
A $p$-adic Brownian motion is a continuous time stochastic process in a $p$-adic state space that has a Vladimirov operator as its infinitesimal generator. The current work shows that any such process is the scaling limit of a discrete time random walk on a discrete group. Earlier work required the exponent of the Vladimirov operator to be in $(1, \infty)$, and the convergence was the weak convergence of probability measures on the Skorohod space of paths on a compact time interval. The current approach simplifies the earlier approach, allows for any positive exponent, eliminates the restriction to compact time intervals, and establishes some moment estimates for the discrete time processes that are of independent interest.
