Asymptotic properties of the estimates of the coefficients in Ornstein-Uhlenbeck processes that are not necessarily stable
Lee Pak Kuen, Philip
THESIS
1998
M.Phil. Mathematics
viii, 59 leaves : ill. ; 30 cm
Abstract
In this paper, we investigate the almost sure asymptotic properties of Ornstein-Uhlenbeck processes that are not necessarily stable. We consider four cases: (1) All the eigenvalues of eF lie outside the unit circle. The process in this case is called purely explosive process. (2) All the eigenvalues of eF lie inside the unit circle. The process in this case is stable process. (3) All the eigenvalues of F are purely imaginary and (4) All the eigenvalues of F are zeros. We finally consider the general Ornstein-Uhlenbeck processes by combining these four cases together.
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