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Feb
22
comment Bounded moments implies finite moments of supremum?
1/4 in $t$ and 1/2 in $x$
Feb
22
revised Bounded moments implies finite moments of supremum?
added 110 characters in body
Feb
22
asked Bounded moments implies finite moments of supremum?
Jan
30
comment Regularity of heat kernel
@charlestoncrabb- Fix a real number $z$ (for example). I want to know how big/small I can make those quantities for $x \neq y \in \mathbb{R}$. I'm not necessarily looking for bounds in that norm. I guess I'm mostly looking for nontrivial upper bounds for these kinds of quantities in the form of powers of the spatial variables ($x,y,z$), and powers of the time variable ($t$), times an exponential. As an example, I want to know if I can bound the last quantity by something like $C |x-y|^a t^{-b}$ times an exponential term, for some constant $C$ and \emph{all} $a \in [0,1]$ and $b \in [1,3/2]$.
Jan
30
awarded  Promoter
Jan
27
asked Regularity of heat kernel
Jan
3
awarded  Yearling
Oct
2
answered What is the Taylor series expansion of $\frac{1}{1-3x-x^2}$?
Sep
21
comment Step in computation of the expected cover time for the simple random walk on a discrete circle
@String - See below for a nice explanation and (an easier alternative)
Sep
21
accepted Step in computation of the expected cover time for the simple random walk on a discrete circle
Sep
21
comment Step in computation of the expected cover time for the simple random walk on a discrete circle
Thanks for your input! The "much easier argument" just occurred to me as well. You explanation of the original argument does make sense though. Cheers!
Sep
21
comment Step in computation of the expected cover time for the simple random walk on a discrete circle
Building on what @String said: $r(k)$ is the average time between hitting the $(k-1)$th distinct vertex and the $k$th distinct vertex. So, I don't think "reaching $r(k-1)$" makes sense
Sep
21
asked Step in computation of the expected cover time for the simple random walk on a discrete circle
Aug
28
answered What is a good book for learning Stochastic Calculus?
Aug
25
comment Expected value of distance between independent Brownian motions
Thanks for the help!
Aug
25
accepted Expected value of distance between independent Brownian motions
Aug
25
asked Expected value of distance between independent Brownian motions
Aug
20
comment Expectation of exponential of integral of absolute value of Brownian motion
I mean, I have $t$ dependence, but can scale the $[0,t]$ integral to $[0,1]$ and have something like your $Y$.
Aug
20
comment Expectation of exponential of integral of absolute value of Brownian motion
Also, your $Y_t$ should just be a $Y$ (there's no $t$ dependence)
Aug
20
comment Expectation of exponential of integral of absolute value of Brownian motion
I actually just came across that paper. Yes, it's not pretty, but this is what I will try. Thanks for your input!