Stitching pairs of L茅vy processes into harnesses

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• 作者：W艂odek Bryc^a ; ^{brycw@math.uc.edu} ; ^{Wlodzimierz.Bryc@UC.edu} ; Jacek Weso艂owski^b ; ^{wesolo@alpha.mini.pw.edu.pl}
• 关键词：60G48 ; 60J99 ; 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：August, 2012
• 卷：122
• 期：8
• 页码：2854-2869
• 文件大小：252 K

摘要

We consider natural exponential families of L茅vy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be 鈥渟titched together鈥?into a single harness. The stitching consists of deterministic reparametrization of the time for both processes, so that they run on adjacent time intervals, and of the choice of the appropriate law at the boundary.

Processes in the L茅vy-Meixner class have an additional property that they are quadratic harnesses, and in this case stitching constructions produce quadratic harnesses on .