Timeline for Laplace transform and fractional moments
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 19, 2022 at 2:43 | history | edited | kjetil b halvorsen | CC BY-SA 4.0 |
added tex code
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| Nov 17, 2009 at 14:31 | comment | added | Piotr Miłoś | Yes, but the problem is that I have the Laplace transform of "whole" X that is F(s). How can I calculate F+ and F- using F only? May be I missing something elementary, but I can not see how to do it in an easy way (of course in principle one can apply the inverse Laplace transform and so on but this is not easy usualy ). | |
| Nov 16, 2009 at 6:18 | comment | added | David Bar Moshe | If you write the Laplace transform of the probability measure of X as a sum of two pieces, the first corresponds to the integral from -inf to 0 and the second from 0 to +inf, i.e., F(s) = F+(s) + F-(s), then the Laplace transform of the probability measure of |X| will be F+(s)+F-(-s), from which you can derive the moments of |X|. | |
| Nov 14, 2009 at 18:07 | comment | added | Piotr Miłoś | I thought about this also. I have even tried to use it but it does not very handy to use. I was hoping for something more "natural". Anyway, I have another question. Let us now drop the assumption that X is positive but assume that the Laplace transform exists. How can one calculate $E|X|$? | |
| Nov 14, 2009 at 16:40 | history | answered | David Bar Moshe | CC BY-SA 2.5 |