18,717 reputation
22861
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 26
visits member for 3 years, 7 months
seen Aug 17 at 14:25

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.


Aug
10
accepted Usual convex combination and the one with measure
Jul
31
accepted Extensions of universal measures
Jul
28
comment Determine whether the following map is a linear transformation.
Linearity is $T(af + bg) = aT(f) + bT(g)$ where $a,b$ are elements of the underlying field
Jul
28
revised Why are those objects initial or final obejcts?
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Jul
28
comment Why are those objects initial or final obejcts?
@RooibosTee: I think your comment better be sarcasm
Jul
28
comment “Unclosure” on a set with binary operation
As much as $1+1\notin X$ for all $1\in X$
Jul
28
comment “Unclosure” on a set with binary operation
You mean, you have a set $S$ and its subsets $X$ and an operation $d$ such that $S$ can be represented through $(X,d)$? I think, one would say that $X$ generates $S$. For example, like positive integers for $S$, $X = \{1\}$ and $d$ for summation, or a related concept of free monoids/groups.
Jul
28
answered Double integral where limits are the first quadrant
Jul
28
comment Prototypical examples of functions in various function spaces
constant functions, and in particular, a constant function $0$, belong to quite a lot of function spaces
Jul
28
answered Probability density use for biased outcome
Jul
28
answered Surjective functions and cal'
Jul
28
comment Finite shannon entropy and mutual information
Distribution of $X$ can have finite entropy, or infinite entropy - that depends on the distribution. It does not depend on whether the distribution is continuous or discrete: there examples of discrete finite entropy distributions, discrete infinite entropy distributions, continuous finite entropy distributions and continuous infinite entropy distributions. In each case, for each given distribution, you have to check whether it has a finite entropy or not, either by your hands, or to google whether somebody have done this for you and put it e.g. in Wikipedia.
Jul
28
comment $\sigma(X_1,\dots, X_n) = \sigma(S_1,\dots, S_n)$ generated by partial sums
I've updated my answer to give a general approach to this class of problems.
Jul
28
revised $\sigma(X_1,\dots, X_n) = \sigma(S_1,\dots, S_n)$ generated by partial sums
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Jul
28
comment Finite shannon entropy and mutual information
Well, normal distribution. Just google any famous continuous distribution you like and go the its Wikipedia page. In most of the cases the formula for entropy would be there. In many cases it is finite.
Jul
28
comment Distributions of local times of a single excursion of 1D random walk
Since it's a Markov Chain, have you tried obtaining recurrence equation for this distribution?
Jul
28
comment Finite shannon entropy and mutual information
Then in the paper I've attached there are some conditions for finite and infinite entropies - is that what you need?
Jul
28
answered Probability density function of two uniformly distributed stochastic variables
Jul
28
revised Probability density function of two uniformly distributed stochastic variables
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Jul
28
comment Finite shannon entropy and mutual information
Well, that would not be a very useful notion then. No, for some particular $X$ and $X,Y$ the entropy and mutual information can be finite. In each case you just compute it, or try to come up with upper bounds. Are you asking about the general case (then that's only that you can get) or you need to show it for some particular example?