Stitching pairs of Levy processes into harnesses

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Bry, Wlodek¹  Wesolowski, Jacek² 

[1] Univ Cincinnati, Dept Math, Cincinnati, OH 45221 USA

[2] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland

关键词: Meixner processes;    Martingale characterization;    Quadratic conditional variances;    Harnesses;    Natural exponential families of Levy processes;   

DOI  :  10.1016/j.spa.2012.05.005

来源: Elsevier

【 摘 要 】

We consider natural exponential families of Levy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be stitched together 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 Levy-Meixner class have an additional property that they are quadratic harnesses, and in this case stitching constructions produce quadratic harnesses on [0, infinity). (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free