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 Mar14 awarded Popular Question Jan16 revised Distribution of $(\sup_{0\leq s\leq t} W_s -W_t)$ edited body Jan16 revised Distribution of $(\sup_{0\leq s\leq t} W_s -W_t)$ added 352 characters in body Jan16 comment Distribution of $(\sup_{0\leq s\leq t} W_s -W_t)$ @Did : Thank you for your answer. I am aware of this result. I am struggling to obtain the law of $g(X_t,W_t)$ where $g(x,w) = x-y$. Jan16 revised Distribution of $(\sup_{0\leq s\leq t} W_s -W_t)$ added 3 characters in body Jan16 revised Distribution of $(\sup_{0\leq s\leq t} W_s -W_t)$ edited tags Jan16 asked Distribution of $(\sup_{0\leq s\leq t} W_s -W_t)$ Dec4 awarded Popular Question Nov24 comment Integral of a geometric Brownian motion Indeed I was not clear at all with my comment. Sorry for that. I would like to know if the law of this random variable is trivially known. If there is the case what is this law? Has its distribution a "simple" analytic formula ? Nov20 comment About an integral equation I haven't assumed $u= s$ for deducing that the integrand is zero. After that if the integrand do is zero for all u between $s$ and $T$ I can look to the equation for $u =s$. The mistake is in deducting that the integrand is zero if it is. And I particularly think it is wrong. The question is "why is it wrong?" Nov18 revised About an integral equation added 459 characters in body Nov18 comment About an integral equation Thanks a lot for you answer. I just realised I permeated the integral on the equation which does not change much for the solution. However it's better to adapt it Nov18 revised About an integral equation added 25 characters in body Nov18 revised About an integral equation deleted 160 characters in body; edited title Nov18 revised About an integral equation deleted 160 characters in body; edited title Nov17 revised About an integral equation added 198 characters in body Nov17 revised About an integral equation added 24 characters in body Nov17 revised About an integral equation edited tags Nov17 revised About an integral equation added 67 characters in body Nov17 revised About an integral equation added 15 characters in body