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.
Thanks for the comments. Yea
"The condition is that g(s) is the Laplace transform of a nonnegative
function. ", Then, any specific requirement for such g(s) to make it
be a Laplace transform of a nonnegative function??
Many Thanks,
[EMAIL PROTECTED] (Robert Israel) wrote in message news:<[EMAIL PROTECTED]>...
> In article <[EMAIL PROTECTED]>,
> ZHANG Yan <[EMAIL PROTECTED]> wrote:
>
> >Suppose that X is nonnegative continuous random variable with
> >probability density function f_X(x).
> >Now, we have
>
> >A = Integral ( InverseLaplace(g(s)) f_X(x), 0, INFINITE)
>
> >where Integral( ..., 0, INFINITE) represents the integral from zero to
> >positive infinite. InverseLaplace(g(s)) represents the inverse
> >laplace of g(s). We can denote that
>
> >G(x) = InverseLaplace(g(s)).
>
> >My question is as follows:
> >If A is greater(or less) than zero, then what condition should the
> >function g(s) satisfy, or any requirement for the function g(s)?
>
> I assume you mean A >= 0 for all such f. I'll also ignore the fact that
> in nontrivial cases there are some f for which the integral diverges.
>
> By taking suitable limits ("approximate delta functions"), you must
> have G(x) >= 0 on [0,infinity). So the condition is that g(s) is the
> Laplace transform of a nonnegative function.
>
> Robert Israel [EMAIL PROTECTED]
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia
> Vancouver, BC, Canada V6T 1Z2
