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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
19
comment Measurability of integrals with respect to different measures
Answered on MO. In future, please don't crosspost so fast. Accepted practice is to wait at least several days.
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...
Apr
10
comment Wrongful conviction Bayesian argument in need of integral-solving talent
@DustinWehr: Good spot. Fixed.
Apr
10
comment Wrongful conviction Bayesian argument in need of integral-solving talent
@DustinWehr: Please don't post to Math.SE right away. This question can be migrated there. If you post a new question there, they will be duplicated, and people who see one will miss the progress made on the other.