7,500 reputation
13068
bio website thatsmathematics.com
location Colorado
age
visits member for 4 years, 4 months
seen 2 hours ago

2h
comment Does a BCL algebra define a partial order?
Did you mean this as an update to your previous answer? It is better to edit your existing answer (there is an "edit" button under your post) rather than adding a new one.
2h
comment Does a BCL algebra define a partial order?
You can use $\LaTeX$ syntax here, thanks to MathJax. That would make your answer much more readable. More details.
11h
comment Is this generating family of a measurable space of point measures a pi-system?
@MaxSuica: The program is in C. It was pretty easy to express; I used bitmasks to encode sets. I can add the code to my answer if you are interested.
1d
comment Probability that d-Brownian Motion ,d>3, avoids a set A
@JoonasIlmavirta: The statement is, with probability 1, there exists a cylinder which is not hit. The cylinder depends on the outcome $\omega$, hence the phrase "random cylinder". This is actually quite a different question than computing the probability of avoiding a fixed set, so I think perhaps the question should be clarified.
Jul
28
comment Can a linear map on a finite-dimensional subspace be extended to the whole space “trivially”?
This question is not research level and should be migrated to math.stackexchange.com. However math.stackexchange.com/questions/135791/… should be helpful.
Jul
23
awarded  Nice Answer
Jul
23
revised Removing an article from arxiv
edited tags
Jul
23
answered Removing an article from arxiv
Jul
22
comment maximum of certain Gaussian processes
You can accept your own answer.
Jul
22
answered Is this generating family of a measurable space of point measures a pi-system?
Jul
22
comment Examples of a continuous martingale with $E[\sup\limits_{0\leq s\leq t} |M_s|]=\infty$?
I'm confused: does $B_t$ start at 0? Then surely $M_t$ is not continuous? And aren't we looking for a martingale, not a local martingale?
Jul
21
comment 27 years old. Working in silicon industry. Considering PhD in Math
@Qfwfq: This wouldn't be a good question for Academia.SE either. Personalized advice is a bad fit for SE in general, and this question is moreover very broad and subjective.
Jul
18
comment Densely-defined unbounded operators with large support
What topology is being put on the set of all unitary operators?
Jul
16
comment Translation is continuous in measure space
@YemonChoi: It certainly does when $f$ is continuous. Otherwise you have to use the fact that the continuous functions are dense in $L^1_{\mu}[T]$. All this is worked out in Folland's Real Analysis, for instance, and so I don't think this is a research level question.
Jul
14
comment How to evaluate the wiener measure of sets?
@supersnail: Perhaps you should rephrase your question, then, to focus on the specific problem that interests you (in particular the title is misleading). But the necessary techniques will depend on what $G$ is. For example, if $G = \mathbb{R}^n - \{p\}$, you are asking about the recurrence and transience of Brownian motion, and that's already a nontrivial fact.
Jul
14
comment Why does it seem that $rca=rba$?
@SeanEberhard: Good example. Moreover, let's call your functional $f$. If $i$ is the inclusion $i : c_0 \to \ell^\infty$, let $i^* : (\ell^\infty)^* \to (c_0)^* = \ell^1$, and you can check that $i^* f = 0$. So we see explicitly that $i^*$ is not injective.
Jul
14
comment Why does it seem that $rca=rba$?
As an elementary mnemonic, if you have a linear map $T : X \to Y$ and $T^*$ is its adjoint, you should expect the injectivity of $T^*$ to be related to the surjectivity of $T$, and vice versa. (Think about matrices with some zero rows or columns.) It's a little trickier in infinite dimenions (e.g. in some cases, instead of "surjective" you want "dense range") but it helps in this case: since the inclusion from $C_0$ to $C_b$ is not surjective (nor does it even have dense range) you should not expect its adjoint to be injective.
Jul
14
comment Intuition for the definition of a probability generator of a Feller process
I do not have the book handy, but I am guessing he will go on to show that if $L$ satisfies these conditions, then it generates a semigroup $P_t$ ((iii) seems to be saying something about the spectrum of $L$ and will probably let you invoke Hille-Yosida) and $P_t$ will have the necessary properties to be a (Feller) transition function, so that $P_t f(x) = E_x f(X_t)$ where $X_t$ is the associated Markov process. (iv) will give you $P_t 1 = 1$ and I suspect (ii) will be related to showing that $P_t$ is positivity preserving.
Jul
14
comment How to evaluate the wiener measure of sets?
I don't think you are really asking the right question here. Asking "In general, how do I compute the Wiener measure of sets" is tantamount to asking "In general, how do I prove theorems about Brownian motion." It is a very large theory and there are a great variety of techniques. Some very deep and difficult theorems (as well as open questions) can be stated as asking for the Wiener measure of a particular easily-described Borel set. So if there's a specific set whose measure you want to know, you should ask that by itself.
Jul
14
comment Commutator with Dirichlet Laplacian
@ChristianRemling: Technically, the identity as stated is only for $C^\infty_0$ functions, which the eigenfunctions are not, so we'd also need an approximation argument.