3,121 reputation
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bio website math.wisc.edu/~janjigia
location Madison, WI
age
visits member for 2 years, 6 months
seen 16 mins ago

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


Apr
9
comment Is convergence in probability to a uniformly continuous function a sufficient condition for stochastic equicontinuity?
What are your thoughts on this? Have you considered what happens if you take $\Theta = [0,1]$ (which is compact) and $g_T$ to be continuous, non-random, uniformly bounded and pointwise convergent to a continuous function, but not uniformly convergent?
Apr
8
comment Coupled stochastic differential equations?
As written, these are random ODEs. Since Brownian motion (and most other processes built from it) is (Holder) continuous you can solve these pathwise the way you are used to. If you wanted to write this with a time derivative of $B$ there, then you would have a coupled family of stochastic differential equations. At this point, it becomes physically important to decide what type of SDE you mean.
Apr
8
reviewed Leave Open Find $\int \limits_0^\pi \sin(\sin(x))\sin(x)\mathrm dx$
Apr
7
reviewed Close Limits of series, proof of the convergence of two sequences
Apr
4
comment Fixed-time Jumps of a Lévy process
What exactly do you mean by "at fixed times"?
Apr
4
comment Use Ito's Lemma to show:
Can you add a statement of what your version of Ito's lemma is? What you have there is a slight rearrangement of what I would take to be the statement of Ito's lemma applied to f(t)B(t).
Apr
4
reviewed Close Properties of arithmetic functions
Apr
3
reviewed Leave Open $x\rightarrow \int_{0}^{x} \frac{\operatorname{sin}(t)}{t}$ is a bounded function
Apr
3
reviewed Close This is a probability mass function problem
Apr
2
comment For the function $Y = e^{-x}$ where $X$ is $N (0,1)$
What have you tried? Is there a specific point where you are getting stuck?
Mar
25
reviewed Close Determine whether the following series convergent?
Mar
24
comment Why is a brownian motion conditioned to stay positive a Bessel-3
Notice that $P(\min_{0 \leq s \leq t}B_s \geq 0) = 0$, so you have to say what you mean by saying "Brownian motion conditioned to stay positive." In the usual interpretation, this result is Pitman's 2M-B theorem. You can find a number of proofs of that result.
Mar
24
comment Why is $e^\pi - \pi$ so close to $20$?
Yeah, that was silly. I meant 19.9991, sorry. My point though is that it's probably just an accident of the fact that we're calling 20 special.
Mar
24
reviewed Close if the imaginary part of an entire function f is bounded, then f is constant.
Mar
23
reviewed Leave Open Seeking intuitive explanation of Clifford Algebra
Mar
22
reviewed Close Property of Homology and orientation
Mar
22
reviewed Close For $x>0$, $x + \frac1x \ge 2$ and equality holds if and only if $x=1$
Mar
22
reviewed Leave Closed Length of median extended to the circumcircle
Mar
22
reviewed Leave Closed Twin Prime Conjecture's Proof
Mar
22
reviewed Looks OK Trig function evaluations. $\frac{\cos^3 (\pi)}{3}$