Nonminimal sets, their projections and integral representations of stable processes

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• 作者：Vladas Pipiras
• 关键词：Stable processes ; Minimal integral representations ; Nonminimal sets ; Projections ; Projective classes ; Mixed moving averages
• 刊名：Stochastic Processes and their Applications
• 出版年：2007
• 出版时间：September 2007
• 年：2007
• 卷：117
• 期：9
• 页码：1285-1302
• 全文大小：345 K

文摘

New criteria are provided for determining whether an integral representation of a stable process is minimal. These criteria are based on various nonminimal sets and their projections, and have several advantages over and shed light on already available criteria. In particular, they naturally lead from a nonminimal representation to the one which is minimal. Several known examples are considered to illustrate the main results. The general approach is also adapted to show that the so-called mixed moving averages have a minimal integral representation of the mixed moving average type.