3,276 reputation
1927
bio website math.wisc.edu/~janjigia
location Madison, WI
age
visits member for 2 years, 11 months
seen 3 hours ago

I am a graduate student in the probability group of the mathematics department at the University of Wisconsin - Madison.


May
1
comment Expectation and variance of correlated exponential brownian motions
What do the differentials inside the exponential mean?
Apr
30
reviewed Close Rational doubt ( doubt in rational number)
Apr
30
revised What is the relation of Lp bound between tightness?
formatting
Apr
30
comment What is the relation of Lp bound between tightness?
How are you defining tightness? I edited your post slightly to improve the formatting. Have I changed the meaning at all?
Apr
23
reviewed Looks OK Uniform convergence of root function
Apr
23
reviewed No Action Needed What's the point of Dirac delta function?
Apr
23
reviewed Leave Open how to show this function doesn't belong to Hilbert space?
Apr
23
comment Covariance between brownian bridge and its max.
I haven't worked this out, but it should be possible to do this with Girsanov. Use the fact that $B(t)$ solves $dB = - \frac{B}{1-t}dt + dW$ on $0 \leq t < 1$ and use Girsanov to rewrite this as a BM. Since the joint distribution of BM and the maximum of BM is known, this reduces the problem to a (possibly computable) integral.
Apr
21
reviewed Leave Open An example of a noncommutative PID
Apr
21
reviewed Close The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
Apr
21
reviewed Close If $f \in L^{\infty}$ and $\exists r < \infty$ so that $\|f\|_r < \infty$, show $\lim_{p \rightarrow \infty} \|f\|_p = \|f\|_{\infty}$
Apr
21
reviewed Close Convergence from $L^p$ to $L^\infty$
Apr
21
reviewed Close The golden ratio in statistics of literature
Apr
21
reviewed Close Real Analysis question about polygons and derivatives
Apr
21
reviewed Close Banach space and it's compact subsets
Apr
20
reviewed Close Proof: $Ax=x$ for all $x$ implies $A=I$
Apr
18
reviewed Close Proving that the set of irrational numbers is uncountable
Apr
18
reviewed Leave Open Equality of integrals: $ \int_{0}^{\infty} \frac {1}{1+x^2} \, \mathrm{d}x = 2 \cdot \int_{0}^{1} \frac {1}{1+x^2} \, \mathrm{d}x $
Apr
18
reviewed Close Mental Math Techniques
Apr
17
comment Is the martingale property preserved by taking weak$^*$-limits?
I think what you are calling weak* convergence is typically called strong convergence of measures in the literature. Unfortunately, I know nothing about that and my previous comment is not relevant, sorry. I was assuming your test functions were continuous. If they were continuous on say $\mathbb{R}^d$, then you could use a Skorokhod representation theorem to realize the sequence as an a.s. limit on a single probability space and uniform integrability would imply $L^1$ convergence.