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 Sep 29 comment $\langle X\rangle_t = t$ Why was this heavily upvoted? Seems to me to be rather offtopic for the site... Sep 25 awarded Citizen Patrol Sep 25 comment Integral of the product of Normal density and cdf @Randel How can you think this is a great answer if you feel there is a gap at the first step, I wonder... Anyway, thanks for the appreciation, and note that $$\int_\mathbb R\Phi(B^{-1}(x-A))\varphi(x)\mathrm dx=E(\Phi(B^{-1}(Y-A)))$$ and that, for every $x$, $$\Phi(x)=P(X\leqslant x),$$ hence, using the independence of $X$ and $Y$, one gets the formula in the post. Sep 16 awarded Nice Answer Jun 28 revised Typical value of totient function added 21 characters in body Jun 22 revised Constructing Bernoulli random variables with prescribed correlation deleted 8 characters in body Jun 18 comment for which values of $\theta$ does this equation $x_{n+1}=\cos(\theta)x^2_{n}-\sin(\theta)x^2_{n-1}$ have bounded solutions? Every ball centered at $0$ with radius at most $1/(|A|+|B|)$ is stable by the dynamics. For every $\theta$, $1/(|A(\theta)|+|B(\theta)|)\leqslant1/\sqrt2$. For every starting point such that $x_{-1}^2+x_0^2\lt1/2$, $x_n\to0$ at least geometrically fast. May 1 revised Brownian local time density deleted 12 characters in body Mar 15 awarded Yearling Sep 26 revised Correlated Brownian motion and Poisson process deleted 9 characters in body Sep 24 awarded Autobiographer Sep 23 revised Top specialized journals added 2 characters in body Sep 6 comment Reference question: Brownian motion and surface area A plane with a greater area than another plane? Brrr... Aug 24 comment Dominating Poisson with parameter depending on a Bernoulli Right, I messed up. Sorry about that. Aug 20 answered Residual lifetime of heavy-tailed random variable Aug 20 revised Measure concentration for law of large numbers deleted 36 characters in body; edited tags Aug 20 comment Stochastic integration by parts to obtain Kailath Segall identity for iterated stochastic integrals? Jul 18 comment Brownian local time density @lost1 No, the local time at 0 does not say anything about the distribution of the time spent above 0. Is this your question? (And no I had not seen the MSE question, whose answer is entirely standard.) Apr 16 comment Is minimum of convex envelope the same as minimum of the original function? @CristóbalGuzmán Nice to see the nonconvexity of $f$ is not a problem anymore. The modification you now suggest is trivial--I am sure you will figure it with pleasure. Apr 16 comment Is minimum of convex envelope the same as minimum of the original function? @CristóbalGuzmán Off-topic. Please refer to my comment dated Nov 15 '12 at 12:19 on Yiyong Feng's post.