Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am solving $I = \int_{0}^{1}f(x)dx$ by Monte Carlo, e.g $I = E[f(U)]$ where $U\sim unif([0,1])$ so have

$I = E[f(U)]\approx \hat I_M\colon= \frac{1}{M}\sum_{m=1}^Mf(u_m)$

I am interested in how quickly $\hat I_M$ converges to $I$, i.e. how quickly $|\hat I_M - I|\rightarrow 0$ as $M\rightarrow \infty$. I do not understand in which convergence sense I am looking at? Is it in simply in 'absolute convergence sense'?

Thanks in advance for any help!

share|cite|improve this question
1  
www.stanford.edu/class/cme308/OldWebsite/notes/chap3.pdf (section 3.6 and especially section 3.8 for the central limit theorem). – Learner Apr 27 '13 at 12:21
    
Awesome thanks! That has really helped – Kane Blackburn Apr 27 '13 at 14:02

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.