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 Dec7 comment application of strong vs weak law of large numbers Can you give an example where weak law holds but strong law does not hold? Dec7 asked application of strong vs weak law of large numbers Nov11 accepted convergence of average of iid random variables Nov11 asked convergence of average of iid random variables Nov4 revised application of Ito's lemma added 144 characters in body; edited body Nov4 asked application of Ito's lemma Nov4 revised derivative of characteristic function added 166 characters in body Nov4 comment convergence of sequence of random variables Wiki page mentions convergence in mean implies convergence in probability. Why is that? Nov4 asked convergence of sequence of random variables Nov4 asked derivative of characteristic function Oct25 accepted sigma algebra generated by random variable Oct25 comment combination of brownian motion Thanks. I have a stock price function that is a stochastic process (e.g. $S = S_0 + B_t$). Now I am interested in finding various option values over those stock prices which involves finding the expectation. So to find asian call value, I need to find $E(\frac{S_1+S_2}{2} - K)^+$ which requires finding the density function $B_1+B_2$ computed by differentiating the distribution function. Hope this makes sense. Oct25 comment Lebesgue Dominated Convergence example Thanks Arturo. The function $f_n(x)$ converges to 0 as $n\to\infty$. So it converges point wise to 0. So the integral as $n\to\infty$ should evaluate to 0 by DCT. Oct25 asked combination of brownian motion Oct25 comment Radon-Nikodym example I got this question from the internet by searching contents on Radon-Nikodym theorem... Oct25 comment Lebesgue Dominated Convergence example Carl - I am going through a couple of books on probability and asking questions from exercises and things I do not understand. I am still in the very basics. If you need reference to the book/article let me know. Oct24 comment sigma algebra generated by random variable To extend the answer, to test independence, we only need to test disjoint sets in the sigma algebra. Then you can use the additivity property of a probability measure to say that any of the other elements in the sigma-algebra works as well. Oct24 comment sigma algebra generated by random variable Got it. Sorry about the confusion. Oct24 asked Radon-Nikodym example Oct24 asked Lebesgue Dominated Convergence example