Stitching pairs of Levy processes into harnesses

摘要

We consider natural exponential families of Levy processes with randomizedparameter. Such processes are Markov, and under suitable assumptions, pairs ofsuch processes with shared randomization can be stitched together into a singleharness. The stitching consists of deterministic reparametrization of the timefor both processes, so that they run on adjacent time intervals, and of thechoice of the appropriate law at the boundary. Processes in the Levy-Meixner class have an additional property that they arequadratic harnesses, and in this case stitching constructions produce quadraticharnesses.