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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!