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Science Forum Index » Statistics - Education Forum » product integral
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| water |
 Posted: Wed Feb 13, 2008 5:17 am |
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f is continuous function.
ProductIntegral_0^t [1 - f(u)du] = exp[- Integral_0^t f(u)du].
why?
Thanks in advance! |
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| Herman Rubin |
| Posted: Wed Feb 13, 2008 1:06 pm |
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In article <d3e10a83-9049-48ac-8d2f-985c0135f856@i7g2000prf.googlegroups.com>,
water <waterloo2005@gmail.com> wrote:
Quote: f is continuous function.
ProductIntegral_0^t [1 - f(u)du] = exp[- Integral_0^t f(u)du].
why?
Use the definition of product integral, and show that the
ratio of the approximations for the same means of subdividing
the interval approaches 1 for all sufficiently fine partitions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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| water |
| Posted: Wed Feb 13, 2008 8:53 pm |
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Guest
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Quote: and show that the
ratio of the approximations for the same means of subdividing
the interval approaches 1 for all sufficiently fine partitions.
can you say more details?
thanks |
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