论文标题
最大不平等和某些应用
Maximal Inequalities and Some Applications
论文作者
论文摘要
最大不平等是一种不平等，它涉及（绝对）至上$ \ sup_ {s \ leq t} | x_ {s} | $或运行最大运行$ \ sup_ {s \ leq t} x_ {s}我们讨论了具有欧几里得空间中值的几类随机过程的最大不平等：Martingales，Lévy过程，Lévy -type-包括feller过程，（复合）Pseudo Poisson过程，稳定的流程和类似于LévyvyVyvy流程的SDE的稳定的流程和型号。使用Burkholder-Davis-Gundy的不平等现象，我们讨论了概率最大估计与分析的最大材料最大功能之间的一些关系。 本文已被接受用于概率调查的出版
A maximal inequality is an inequality which involves the (absolute) supremum $\sup_{s\leq t}|X_{s}|$ or the running maximum $\sup_{s\leq t}X_{s}$ of a stochastic process $(X_t)_{t\geq 0}$. We discuss maximal inequalities for several classes of stochastic processes with values in an Euclidean space: Martingales, Lévy processes, Lévy-type - including Feller processes, (compound) pseudo Poisson processes, stable-like processes and solutions to SDEs driven by a Lévy process -, strong Markov processes and Gaussian processes. Using the Burkholder-Davis-Gundy inequalities we als discuss some relations between maximal estimates in probability and the Hardy-Littlewood maximal functions from analysis. This paper has been accepted for publication in Probability Surveys
