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 Aug2 awarded Popular Question Jul2 awarded Curious May5 awarded Tumbleweed Apr28 asked Condition on initial value of stochastic process Mar12 comment Differentiability of function defined as integral Nice. Thank you very much. Is there any way to determine the (non-)differentiability of $F$ without actually computing $$\int_0^1 \frac{f(t,h) - f(t,0)}{h} dt$$ ? My question is coming from a real problem where I can compute derivatives of $f$ w.r.t $x$ but cannot explicitly integrate $f$ w.r.t $t$. Mar12 accepted Differentiability of function defined as integral Mar11 asked Differentiability of function defined as integral Sep12 asked Ito vs Stratonovich SDE with irregular time-dependence in coefficients Jul2 comment Prove the density of this SDE is not smooth in a parameter thank you for your answer. I don't quite see how it helps with determining smoothness in the variable $x$, though. Jun28 awarded Promoter Jun26 asked Prove the density of this SDE is not smooth in a parameter Apr9 answered Martingale inequality Apr7 comment Martingale inequality Well, the inequality holds for all fixed $r$. And, assuming $f$ is continuous in the first variable, I think that for a given $t$, $Y^r_t$ and $Y^t_t$ should be close when $r$ is close to $t$. However, I am not sure if the same is true of $\sup_{t \in [0,T]} Y^r_t$ and $\sup_{t \in [0,T]} Y^t_t$ or the quadratic variations. Apr7 comment Martingale inequality @Did I have found a reference: see proposition 4.24 here statslab.cam.ac.uk/~beresty/teach/StoCal/sc3.pdf Apr7 comment Martingale inequality @Did My source is a paper by Kusuoka & Stroock (Applications of the Malliavin calculus. II) which is not available online, but the inequality comes from viewing the martingale as Brownian Motion run at the "clock" of its quadratic variation, using the distribution the running max of a Brownian Motion and using Gaussian tail estimates. Apr6 asked Martingale inequality Aug29 accepted Roll six dice. Probability of at least one pair. Aug29 asked Roll six dice. Probability of at least one pair. Jun18 awarded Commentator Jun18 comment Are affine SDEs invertible? @mike : Sorry, I see what you are saying now. Do you have a reference for proving that say $X_t = x + \int_0^t a_s ds + \int_0^t b_s dW_s$ hits zero a.s.?