Barndorff-Nielsen, Ole Eiler^{4}; Stelzer, Robert^{3}

Affiliations:

^{1} Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University^{2} Department of Mathematics, Science and Technology, Aarhus University^{3} Technical University Munich^{4} Department of Mathematics, Science and Technology, Aarhus University

Abstract:

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 ItÃ´ 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.

Type:

Journal article

Language:

English

Published in:

Probability and Mathematical Statistics, 2007, Vol 27, Issue 1, p. 3-43