论文标题
限制一般引导随机步行的定理和终身制度
Limit theorems and ergodicity for general bootstrap random walks
论文作者
论文摘要
考虑到简单的对称随机步行$（x_n）_ {n \ ge0} $的增量，我们将这些增量回收为简单的对称随机步行$（y_n）_ {n \ ge0} $适用于$（x_n）_ {n n \ ge0} $。我们研究适当归一化的二维过程的长期行为$（（x_n，y_n））_ {n \ ge0} $。特别是，我们为该过程提供了必要和充分的条件，以使二维布朗运动（可能是退化）。我们还讨论了极限不是高斯的案例。最后，我们为回收转化的终身制提供了一种简单的必要条件，从而使Dubins和Smorodinsky（1992）和Fujita（2008）的概括结果概括了结果，并解决了将军转化的Ergodicity的开放性问题的离散版本（请参见Mansuy和Yor，2006年）。
Given the increments of a simple symmetric random walk $(X_n)_{n\ge0}$, we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{n\ge0}$ adapted to the filtration of $(X_n)_{n\ge0}$. We study the long term behavior of a suitably normalized two-dimensional process $((X_n,Y_n))_{n\ge0}$. In particular, we provide necessary and sufficient conditions for the process to converge to a two-dimensional Brownian motion (possibly degenerate). We also discuss cases in which the limit is not Gaussian. Finally, we provide a simple necessary and sufficient condition for the ergodicity of the recycling transformation, thus generalizing results from Dubins and Smorodinsky (1992) and Fujita (2008), and solving the discrete version of the open problem of the ergodicity of the general Lévy transformation (see Mansuy and Yor, 2006).
