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bio website math.uvic.ca/faculty/aquas
location University of Victoria
age 47
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The pic is the phase portrait of a simple "piecewise isometry". Define a map by sliding the two halves of the plane: the top half to the right; the lower half to the left and then rotate. Around each periodic point of the map there's a "periodic island". These are what are in the image...

Apr
23
answered p-adic analogue of the Strong Law of Large Numbers
Apr
21
awarded  Nice Question
Apr
21
comment Disprove this Piece of Jensen's Inquality “Black Magic”
So this is pretty hopeless. If $g$ is the constant 1 and $h$ takes values 0 and $\pi$, then the right side has cancellation whereas the left side doesn't (so the inequality goes the other way). On the other hand, if $h=0$ and $g$ is non-constant real, then the inequality holds as written. So no inequality of this type exists either way around.
Apr
17
comment Integer solution to the equation
Ummm.. (1) this is not linear algebra; and (2) where does this problem come from?
Apr
16
comment Rate of convergence in the Law of Large Numbers
So I did look at Durrett. I have a paper copy that does not seem to include Thm 2.5.8, but the online version is as you say; and also includes an answer to the other question I asked. Thanks again.
Apr
16
accepted Rate of convergence in the Law of Large Numbers
Apr
16
comment Rate of convergence in the Law of Large Numbers
Thanks very much. That's really great.
Apr
16
comment Rate of convergence in the Law of Large Numbers
OK. Thanks a lot. I'll look in Durrett tomorrow.
Apr
16
comment Rate of convergence in the Law of Large Numbers
Thanks - but isn't Var$(Y_i)$ infinite?
Apr
16
comment Rate of convergence in the Law of Large Numbers
So it doesn't seem likely that $\mathbb E|X|^\alpha<\infty$ will be sufficient for the averages to converge to the $\alpha$-stable law: after all if this condition holds, then so does $\mathbb E|X|^\beta<\infty$ for $\beta<\alpha$. As far as I could tell (without claiming to really understand it), it looked as though the things proved to be in the domain of attraction of the $\alpha$-stable law had infinite $\alpha$th moments (the $\alpha$-stable law certainly has this property).
Apr
16
revised Rate of convergence in the Law of Large Numbers
sharpen question
Apr
16
comment Rate of convergence in the Law of Large Numbers
Thanks @Igor. This does seem very close to my question. I'll see if I can extract a Chebyshev-like result (which is what I really want) from this.
Apr
16
comment Rate of convergence in the Law of Large Numbers
Sorry @NateEldredge for the misunderstanding. So yes. I hope that a K-G stable law limit theorem would do the trick. It's just that I did not find a reference for such a theorem that didn't have a bunch of extra conditions (about slowly varying densities etc). If you know where I can find a statement of the type you're mentioning, that will probably resolve (at least the first part of) my issue.
Apr
16
comment Rate of convergence in the Law of Large Numbers
@Nate: Don't you need a second moment condition to apply CLT?
Apr
16
comment Rate of convergence in the Law of Large Numbers
Thanks @Taha. So I think Bernstein inequalities are based on exponential moments (which diverge in my setting); I was unable to pick out useful results from the paper by the French authors either.
Apr
15
asked Rate of convergence in the Law of Large Numbers
Apr
15
comment Uniquely ergodicity and polynomial ergodic average
I believe the OP is asking about everywhere convergence. I don't see that addressed in HK.
Apr
12
comment SDEs: Bounding the variance of a solution
If I had to guess, I would expect that you would need additional monotonicity conditions on $\sigma$ (e.g. $\sigma_{X,t}(x)$ and $\sigma_{Y,t}(x)$ are monotonic in $t$ and $x$) to make something like this work. Then I would look for a coupling proof.
Apr
12
comment How many values determine a norm?
There is a detailed answer below, but the rough answer is very simple. There is a bijective correspondence between norms and bounded symmetric convex sets containing a neighbourhood of the origin. (the set is the unit ball of the norm; the norm is the Minkowski functional of the set).
Apr
9
awarded  Nice Answer