Nate Eldredge
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 1d comment Can we da/dr*dr/dt to get da/dt It's hard to understand what you are asking. Can you be more specific about what the functions / variables $F,r,t,a$ are, and exactly how they depend on one another? If $a$ is only a function of $r$, then this is just the chain rule; but if $a$ is a function of more variables, and some of them also depend on $t$, then you need more terms. 1d comment Does absolute continuity imply no stochastic domination? What does it mean for a measurable space to be "continuous"? 1d comment How to debug math? I think the "good examples" is actually quite a close analogy for unit testing. Run your code on the input that seems most likely to break it - test the corner cases. Apr 29 comment Discontinuity points of a Distribution function @Daveddd: $\mathbb{Q}$ is the set of rational numbers. I suppose you have seen a proof that this is countable, as it's a fundamental fact; if somehow not, see math.stackexchange.com/questions/659302/… Apr 27 comment Can we apply an Itō formula to find an expression for $f(t,X_t)$, if $f$ is taking values in a Hilbert space? Well, I don't have a copy handy, but I have a note that it discusses stochastic calculus of Hilbert-space valued processes, so I thought it might have an appropriate version of Ito's formula. Apr 27 comment Can we apply an Itō formula to find an expression for $f(t,X_t)$, if $f$ is taking values in a Hilbert space? Another book to check is Michel Metivier, Semimartingales. Apr 25 awarded Revival Apr 25 answered Example of a Continuous-Time Markov Process which does NOT have Independent Increments Apr 21 comment Bizarre failure of integrating factor in elementary differential equation Oh, I think all my $x$ values above are off by $\pi/2$ or so, I mixed up tangent and cotangent. But you get the idea. I guess what I am saying is that in applications, you would always restrict the domain, and the author of the book may have a (stated or unstated) standing assumption that this is what will be done. So I'm not really bothered by it as much as you are - "completely wrong" seems a little harsh to me. Apr 21 comment Bizarre failure of integrating factor in elementary differential equation Alternatively, the "correct" answer is correct over $(-\pi/2, \pi/2)$. For instance, if we were given an initial value $y(0)=y_0$, the solution would be uniquely determined over that interval, but not beyond. But that's probably what you would want for a real-life application - you know your physical system is going to explode at time $\pi/2$, so what's the point in asking what happens after that? This is pretty common - you only care about what happens up until the next singularity, and the given answer is consistent with that. Apr 21 comment Bizarre failure of integrating factor in elementary differential equation The point is that the "correct answer" you gave isn't really the correct answer. For instance, the function $$y(x) = \begin{cases} -\cot(x)+3 \csc(x), & -\frac{\pi}{2} < x < \frac{\pi}{2} \\ -\cot(x) + 4 \csc(x), & \text{otherwise}\end{cases}$$ is a solution of the given equation, but it isn't of the form given in the "correct" answer. Apr 18 awarded general-topology Apr 11 comment Can $C^\infty(\mathbb{T})$ become a Banach space? For instance, the new norm might induce a completely different topology than the original metric. Operations like multiplication, differentiation, integration, might not be continuous under the new norm. Is that really what you want? Apr 11 awarded Nice Answer Apr 11 comment Is there a locally compact, locally connected, Hausdorff and second countable space that is “nowhere locally Euclidean”? How does one see that these are locally connected? Apr 11 comment Wrongful conviction Bayesian argument in need of integral-solving talent @GerryMyerson: I commented above on two bugs in Ben McKay's code. After fixing those, his code gives the same answer as mine. Apr 11 comment Wrongful conviction Bayesian argument in need of integral-solving talent As pointed out by Robert Israel, the region should be $0 < q_1 < q_3 < q_2 < 1$ (unless that was a typo by the OP). Also, your definition of $f$ has $q_3$ twice; the first one should be $q_2$. Making those changes, I get the same result in Sage as in my Mathematica below. See cloud.sagemath.com/projects/… Apr 11 comment Wrongful conviction Bayesian argument in need of integral-solving talent @RobertIsrael: Fixed... :-) Apr 10 comment Wrongful conviction Bayesian argument in need of integral-solving talent So in fact, the most difficult part of doing this integral was typing it in correctly! Apr 10 comment Wrongful conviction Bayesian argument in need of integral-solving talent @GerryMyerson: Oh, I spotted another mistake in mine, my f3 integral has the wrong bounds. Fixing...