POSITIVE-DEFINITE MATRIX PROCESSES OF FINITE VARIATION
Ole Eiler Barndorff-Nielsen
Robert Stelzer
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 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.
2000 AMS Mathematics Subject Classification: 15A52, 60H20, 60G52.
Key words and phrases: Finite variation process, Itô formula, Lévy process,
matrix subordinator, Ornstein-Uhlenbeck type process, positive definite square root.