- #1

trelek2

- 88

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I need help with the monte carlo integration: reliability of the error estimate for functions that are not square integrable.

I'm supposed to investigate this topic.*Hence my first question is what is a function that is not square integrable? I found that such a function is 1/sqrt(x) on the interval 0 to 1. Apparently a function is not square integrable if the integral of its absolute value squared is not finite on that integral... I thought the for f(x)= 1/sqrt(x) that will be -1?

Anyway I evaluated the integrals for 1/sqrt(x) from 0 to 1 (which is 2 analytically) for dofferent number of sample points. Indeed the estimated errors are nowhere close the actual errors...

Can anyone explain why does this happen? And why is 1/sqrt(x) not square integrable?