On Weighted Tempered Moving Averages Processes

Abstract

In this article we introduce a new class of processes: the weighted tempered moving averages processes, which include the tempered moving averages processes as a particular case. They generalize the class of tempered moving averages process which is widely known and has many applications. In some cases they share with the tempered Lévy process the following property: in a close time-frame they behave like an α-stable process while in a long time frame like a gaussian process. Additionally we prove that under certain conditions they are mixing and hence ergodic.