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Multidimensional process of Ornstein-Uhlenbeck type with nondiagonalizable matrix in linear drift terms

Published online by Cambridge University Press:  22 January 2016

Ken-Iti Sato ,
Toshiro Watanabe ,
Kouji Yamamuro  and
Makoto Yamazato
Ken-Iti Sato*
Affiliation:
Department of Mathematics, College of General Education Nagoya University, Nagoya, 464-01, Japan
Toshiro Watanabe
Affiliation:
Center for Mathematical Sciences, The University of Aizu, Ikki-machi, Aizu-Wakamatsu Fukushima, 965, Japan
Kouji Yamamuro
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Nagoya, 464-01, Japan
Makoto Yamazato*
Affiliation:
Department of Mathematics. Nagoya Institute of Technology, Nagoya, 466, Japan
*
School of Informatics and Sciences, Nagoya University, Nagoya, 464-01, Japan
Departmemt of Mathematics, Ryukyu University, Okinawa, 903-01, Japan
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Let Rd be the d-dimensional Euclidean space where each point is expressed by a column vector. Let | x | and ‹x, y› denote the norm and the inner product in Rd. Let Q = (Qjk) be a real d × d-matrix of which all eigenvalues have positive real parts. Let X be a process of Ornstein-Uhlenbeck type (OU type process) on Rd associated with a Levy process {Z: t ≥ 0} and the matrix Q. Main purpose of this paper is to give a recurrence-transience criterion for the process X when Q is a Jordan cell matrix and to compare it with the case when Q is diagonalizable. Here by a Levy process we mean a stochastically continuous process with stationary independent increments, starting at 0.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 141 , March 1996 , pp. 45 - 78
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

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