18,263 reputation
22861
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 26
visits member for 3 years, 6 months
seen 1 hour ago

I am a PhD student at TU Delft, working in applied probability and stochastic optimal control. My current focus is on approximate model-checking of stochastic systems via bisimulations (a part of computer science). I am interested in a wide field of applications, in particular in some areas of finance, such as risk theory.


5h
answered partition with infinite entropy?
5h
comment partition with infinite entropy?
That I'm not sure I understand: the entropy of a discrete distribution does not depend on its underlying space, so you shall be able to assume the mean to be anything.
5h
comment Cantor diagonalization and fundamental theorem
I guess, some of your elements in your list are equivalent (as natural numbers). However, to state it precisely I need to know what is $D_{ij}$, that is what is $D_{11},D_{12}$ etc. From your current setting this is not clear.
6h
comment partition with infinite entropy?
Since $\sum m(I_i) = 1$, the question can be equivalently restated as follows: is there a probability distribution on $\Bbb N$ whose entropy is infinite. As far as I understand, the answer is no as follows from here.
6h
revised Estimating the $(N-1)$- Hausdorff measure of $\Omega\cap \partial B(0,r)$ when $\lim_{r\to\infty} m(\Omega\cap B(0,r))/m(B(0,r))=0$.
edited tags
6h
comment Alternative proof for the fact that a continuous function on a closed interval attains its boundaries.
@ThomasAndrews: perhaps, you mean if $f(x)<M$
7h
comment Terminology on pullbacks
@DanielRust: thank you
7h
accepted Terminology on pullbacks
7h
comment Terminology on pullbacks
factorization sounds good, say $f$ factors as $g\circ h$, thanks
8h
comment Terminology on pullbacks
Thank, would you say there is no special term in the first case?
9h
comment Logarithmic question
@Tunk-Fey: $\log$ conventions are sometimes confusing. In Russia $\log_a$ is used only with a specified base, there is no just $\log$. Also, $\ln x := \log_{\mathrm e}x$, $\lg x := \log_{10} x$. I never heard of $\log_2$ having a special notation in Russian, but Wikipedia suggests it is $\mathrm{lb}\, x$. I can imagine, in other countries conventions are different.
9h
revised Fredholm index for 1-d Schroedinger operator
rolled back to a previous revision
9h
revised Fredholm index for 1-d Schroedinger operator
deleted 3 characters in body
9h
asked Terminology on pullbacks
10h
comment Expectation of e^(cX) if X is a geometric Brownian motion
See the solution here
11h
reviewed Approve suggested edit on Definite integral involving powers and logarithm
11h
asked Ultrametric space of stochastic filtration
12h
comment Upper bounding a Poisson Process with indicators of exponentials
Let us continue this discussion in chat.
12h
answered Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?
13h
comment Why “One cannot construct more than countably many independent random variables”?
In fact, the range of $\xi$ is the only thing that matters - you can define any dependence structure between $\xi_i$'s. Only in case you'd like them to take values from arbitrary measurable spaces and yet have an arbitrary dependence structure, you need to work with a countable $I$ and apply Ionescu Tulcea theorem.