bio | website | math.uvic.ca/faculty/aquas |
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location | University of Victoria | |
age | 47 | |
visits | member for | 4 years, 5 months |
seen | 7 hours ago | |
stats | profile views | 3,897 |
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 |
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Integer solution to the equation
Ummm.. (1) this is not linear algebra; and (2) where does this problem come from? |
Apr 16 |
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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 |
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Rate of convergence in the Law of Large Numbers
Thanks very much. That's really great. |
Apr 16 |
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Rate of convergence in the Law of Large Numbers
OK. Thanks a lot. I'll look in Durrett tomorrow. |
Apr 16 |
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Rate of convergence in the Law of Large Numbers
Thanks - but isn't Var$(Y_i)$ infinite? |
Apr 16 |
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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 |
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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 |
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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 |
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Rate of convergence in the Law of Large Numbers
@Nate: Don't you need a second moment condition to apply CLT? |
Apr 16 |
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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 |
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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 |
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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 |
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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 |