T:A:L:K:S

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title:
Multivariate SupOU Processes
name:
Stelzer
first name:
Robert
location/conference:
levy10
PREPRINT-link:
http://www.e-publications.org/ims/submission/index.php/AAP/user/submissionFile/5327?confirm=4e9c2fa7
abstract:
Multivariate supOU processes are defined using a Lévy basis on the real numbers times the set of square matrices with all eigenvalues having strictly negative real parts. We discuss the existence, the finiteness of moments, the second order structure and important path properties, noting that the peculiarities of the underlying matrices cause new phenomena and features compared to the known univariate case. In particular, we give precise conditions for the validity of an analogue to the stochastic differential equation satisfied by Ornstein-Uhlenbeck type processes, which has been conjectured in the univariate case by Barndorff-Nielsen [2001, Superposition of Ornstein-Uhlenbeck type processes, Theory Probab. Appl. 45, 175-194], but not yet been proven. Our results also imply conditions when supOU processes are compatible with semimartingale integration theory.

Furthermore, we discuss the possible occurrence of long memory in multivariate supOU processes and applications of them.

This talk is based on joint work with Ole Eiler Barndorff-Nielsen Aarhus University.