Positive-definite matrix processes of finite variation

• Autorzy: Barndorff-Nielsen O. E. , Stelzer R.
• Języki publikacji: EN

Abstrakty

EN

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 It8 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.

Słowa kluczowe

EN

finite variation process; Itô formula; Lévy process; matrix subordinator; Ornstein-Uhlenbeck type process; positive definite square root

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 1
• Strony: 3--43
• Opis fizyczny: Bibliogr. 49 poz.

Twórcy

autor

Barndorff-Nielsen O. E.

• Department of Mathematical Sciences, University of Århus, Ny Munkegade, DK-8000 Arhus C, Denmark

autor

Stelzer R.

• Graduate Programme, Applied Algorithmic Mathematics, Centre for Mathematical Sciences, Munich University of Technology, Boltzmannstraße 3, D-85747 Garching, Germany

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