Given $X_1,\cdot ,X_N$ random variables whose joint distribution is given as $\mu$ we will use the Martingale Method to show any Lipshitz Function $f$ over these random variables is subgaussian. The Variance parameter however can have a simple expression under certain conditions. For example under the assumption that the random variables follow a Markov Chain and that the function is Lipschitz under a Weighted Hamming Metric. We shall conclude with certain well known techniques from concentration of suprema of random processes with applications in Reinforcement Learning

翻译：基于 $X_1,\\ cddot, X_N$ 随机变量,其联合分布以 $\ mu美元计,我们将使用 Martingale 方法来显示在这些随机变量上的任何Lipshitz函数 $f$f$, 这些随机变量上的任何利普什兹函数都是 subgaussian 。 然而, 差异参数在某些条件下可以有一个简单的表达方式。 例如,假设随机变量跟随 Markov 链, 且该函数在微弱的Hamming 度下是 Lipschitz 。 我们将以某些已知的技术来结束, 这些技术来自随机过程的精度集中和强化学习的应用。