标题： 自相似性与随机过程族的Lamperti收敛 显示英文标题

标题： Self-Similarity and Lamperti Convergence for Families of Stochastic Processes

摘要： 我们为一参数随机过程族定义了一种新的自相似类型，这种类型适用于许多在传统意义上不是自相似的重要过程族。 这包括作为Hougaard Lévy过程移动平均线定义的新一类分数Hougaard运动，以及一些著名的Hougaard Lévy过程族，如泊松过程、带漂移的布朗运动和逆高斯过程。 这类过程与普通自相似过程有许多共同特性，包括它们的协方差函数的形式，以及它们作为随机过程族的Lamperti型极限定理中的极限出现的事实。 显示英文摘要

摘要： We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of fractional Hougaard motions defined as moving averages of Hougaard L\'evy process, as well as some well-known families of Hougaard L\'evy processes such as the Poisson processes, Brownian motions with drift, and the inverse Gaussian processes. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.