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Contents of PMS, Vol. 27, Fasc. 1,
pages 3 - 43
 

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 r -th power with 0 < r < 1 ) 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.

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