Positive-definite matrix processes of finite variation
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 It formula for finite variation processes. Moreover, Ornstein-Uhlenbeck type processes taking values in the positive semidefinite matrices are introduced and their probabilistic properties are studied.
finite variation process, Itô formula, Levy process, matrix subordinator, Ornstein- Uhlenbeck type process, positive definite square root