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| A Remark on the Condition of Integrability in Quadratic Mean for the SecondOrder Random Processes |
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Citation： |
Wang Zhenpeng.A Remark on the Condition of Integrability in Quadratic Mean for the SecondOrder Random Processes[J].Chinese Annals of Mathematics B,1982,3(3):349~352 |
| Page view： 873
Net amount： 808 |
Authors： |
Wang Zhenpeng; |
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| Abstract： |
In quite a few publications(eg.[1,2,3])there is the theorem
$[\int_a^b {\xi (t)dt(in{\rm{ q}}{\rm{.m}}{\rm{.)}}} \]$exists if and only if
$[(R)\int_a^b {\int_a^b {\Gamma (s,t)dsdt} } \]$exists,
where $\xi(t),t \in [a,b]$ is a second order random process and
$\Gamma(s,t)=E[\xi(s)\overline {\xi (t)}],s,t \in [a,b]$.
However,the necessary condition does not hold,that is to say:the integral in q.m.
$\int_a^b {\xi(t)dt}$exists but the Riemann integral (r)\int_a^n{\int_a^b{\Gamma(s,t)dsdt}} can not exist.A counter example is constructed to substantiate this point. |
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