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| ON THE GERM-MARKOV PROPERTY OF THE GENERALIZED N-PARAMETER ORNSTE IN-UHLENBECK PROCESS |
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Citation： |
Luo Shoujun.ON THE GERM-MARKOV PROPERTY OF THE GENERALIZED N-PARAMETER ORNSTE IN-UHLENBECK PROCESS[J].Chinese Annals of Mathematics B,1989,10(1):65~73 |
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Net amount： 820 |
Authors： |
Luo Shoujun; |
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| Abstract： |
A generalized N-parameter Ornstein-Uhlenbeck process $(\[GOU{P_N}\])$ is defined as $$\[X(t) = {[f(t)]^{ - 1}}\int_a^t {f(s)\eta (ds)} \]$$,
$\[t \in R_a^N\]$, where $\[a = (0, \cdots ,0)\]$ or $\[( - \infty , \cdots - \infty )\]$, correspondently $\[R_a^N = R_ + ^N\]$ or $\[{R^N}\]$ ,and $\[\eta (ds)\]$ is the standard Gaussian orthogonal random measure and $f$ is an infinitely differentiable and locally qnadratically integrable positive function. In this paper it is proved that the $\[GOU{P_N}\]$ has the so called germ-Markov property with respect to any bounded domain, and
two examples are given which say that for spherical and some pyramid-like domains, the minimal splitting $\[\sigma \]$-algebras for the "interior" and the "outer" information $\[\sigma \]$-algebras are strictly “larger” than the boundary information $\[\sigma \]$-algebras. |
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