Multivariate generalized Ornstein-Uhlenbeck processes

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• 作者：Anita Behme ; ^{a.behme@tu-bs.de} ; Alexander Lindner¹ ; ^{a.lindner@tu-bs.de}
• 关键词：60G10 ; 60G51
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：April, 2012
• 卷：122
• 期：4
• 页码：1487-1518
• 文件大小：357 K

摘要

De Haan and Karandikar (1989)聽 introduced generalized Ornstein-Uhlenbeck processes as one-dimensional processes which are basically characterized by the fact that for each the equidistantly sampled process satisfies the random recurrence equation , , where is an i.i.d. sequence with positive for each . We generalize this concept to a multivariate setting and use it to define multivariate generalized Ornstein-Uhlenbeck (MGOU) processes which occur to be characterized by a starting random variable and some L茅vy process in . The stochastic differential equation an MGOU process satisfies is also derived. We further study invariant subspaces and irreducibility of the models generated by MGOU processes and use this to give necessary and sufficient conditions for the existence of strictly stationary MGOU processes under some extra conditions.