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bio website math.wisc.edu/~janjigia
location Madison, WI
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visits member for 2 years, 10 months
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I am a graduate student in the probability group of the mathematics department at the University of Wisconsin - Madison.


1d
reviewed Leave Open How prove this diophantine equation $x^2+y^2+z^3=n$ always have integer solution
1d
reviewed Close Proving uniqueness of $e$
1d
reviewed Close Show that all recursively enumerable sets are definable in arithmetic
1d
reviewed Close Calculation: Emotional Contagion
Nov
19
comment The measure generated by the Cantor staircase and the intersection of the Cantor set with its translate
Sorry, yes I was not reading carefully enough.
Nov
19
comment The measure generated by the Cantor staircase and the intersection of the Cantor set with its translate
Think of the Cantor set as $\sum_{k=1}^\infty \frac{2x_k}{3^k}$ where $x_k \in \{0,1\}$. This identifies the set with the compact group $\mathbb{Z}_2^{\mathbb{N}}$. The Cantor measure is a Haar measure with respect to that group structure.
Nov
19
comment The measure generated by the Cantor staircase and the intersection of the Cantor set with its translate
I think that this is going to depend on $\alpha$. You can work out a partial result from the fact that the Cantor measure is Haar with respect to its natural group structure, though.
Nov
2
reviewed Close proof that p implies q entails not p or q
Oct
29
reviewed Close which of the following can be a differential solution for $\frac{dy}{dt}= -Cy$
Oct
29
reviewed Close probability density function question for logs
Oct
29
comment The ito integral is gaussian
The distributional limit normally distributed random variables is (possibly degenerate) normal. See math.stackexchange.com/questions/232540/…
Oct
28
awarded  Enlightened
Oct
28
awarded  Nice Answer
Oct
23
comment In frequentism, does every event have a probability?
Not measurable with respect to what? Probability is not analysis. When you specify a sigma algebra on your underlying space in probability, you are saying something about what events are accessible to your experiment.
Oct
23
comment how to related a weakly convergent random variable with its k-th moment
Whenever you have convergence in distribution of real random variables, you can switch probability spaces and make it almost sure convergence. This is called the Skorokhod representation theorem. Your question is then whether or not convergence a.s. implies convergence of integrals, which is not true in general. A necessary and sufficient condition for $L^k$ convergence (which implies what you want) is uniform integrability. This is slightly stronger than just having convergence of the expectations though.
Oct
23
comment how to related a weakly convergent random variable with its k-th moment
This result holds if the family $\{S_n^k\}_{n=1}^\infty$ is uniformly integrable.
Oct
17
comment Spotting mistake: unnecessary given condition
@PatrickDaSilva This is pretty fundamentally different from your example. Preference relations are the first topic covered in a first course in graduate microeconomics using the standard textbook (MWG). I've never heard of any physics program that starts with elliptic curves.
Oct
2
comment Can $\|f\|_p\to\infty$ arbitrarily slowly? (Looking for hints.)
This is a great classical analysis question. Hints: You may assume without loss of generality $\Phi(p)$ is as regular as you like (continuous for example). Consider a step function on a disjoint partition of $(0,1)$ and choose your coefficients and the measure of the sets in the partition carefully.
Sep
28
reviewed Close Can I use theorems that are beyond the scope of my class in my CBSE exams?
Sep
28
reviewed Close Is the product of i.i.d integrable random variables also integrable?