Timeline for Expectation of $(c+e^{N(0,\sigma^2)})^{-n},\, n>0$
Current License: CC BY-SA 3.0
3 events
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| Mar 11, 2013 at 18:49 | comment | added | Robert Israel | Another possibility is to use Laplace's method, expanding around the maximum of the integrand $\dfrac{(c+e^x)^{-n}}{\sqrt{2\pi} \sigma} e^{-x^2/(2 \sigma^2)}$, which is at the real root of $(n \sigma^2 + x) e^x + c x$. | |
| Mar 6, 2013 at 5:06 | comment | added | user9121 | Thank you for the answer. Unfortunately $c$ is fixed and small so this is not so useful for me (I also found a couple of ways to derive this asymptotic series). | |
| Mar 5, 2013 at 8:21 | history | answered | Robert Israel | CC BY-SA 3.0 |