1 Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University2 Department of Mathematics, Science and Technology, Aarhus University3 Technical University Munich4 Department of Mathematics, Science and Technology, Aarhus University
Processes of finite variation, which take values in the positive semidefinite matrices and are representable as the sum of an integral with respect to time and one with respect to an extended Poisson random measure, are considered. For such processes we derive conditions for the square root (and the -th power with ) to be of finite variation and obtain integral representations of the square root. Our discussion is based on a variant of the Itô formula for finite variation processes. Moreover, Ornstein-Uhlenheck type processes taking values in the positive semidefinite matrices are introduced and their probabilistic properties are studied.
Probability and Mathematical Statistics, 2007, Vol 27, Issue 1, p. 3-43