558 reputation
216
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 26
visits member for 3 years, 4 months
seen Mar 24 at 10:33

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.


Mar
24
comment Universally measurable sets and weak topology
that was quite some time ago, but did you happen to find the answer to the second question of yours? Bertsekas and Shreve do not seem to contain it.
Mar
17
asked Existence of a conditional distribution
Jan
16
comment Commutativity of convex hulls and closed balls
Thanks, my example is very similar to yours I think - at least I also played with the triangle.
Jan
16
accepted Commutativity of convex hulls and closed balls
Jan
16
comment Commutativity of convex hulls and closed balls
I see: I haven't added the intersections with $X$ in the OP from the beginning, sorry. In the current correct formulation I believe there is a counterexample, exactly due to the reason that we cannot translate without leaving $X$ in some cases.
Jan
16
revised Commutativity of convex hulls and closed balls
added 36 characters in body
Jan
15
comment Commutativity of convex hulls and closed balls
Well, here it happens that $y_i$ may not belong to $X$. I thought of shifting by $y-z$, but then it's exactly the problem.
Jan
15
asked Commutativity of convex hulls and closed balls
Jan
14
comment Existence of a map connecting two marginals of a product measure
@MichaelGreinecker: thanks, but Nate's example (appied to $X$ being an arbitrary finite set and $\bar X = [0,1]$) is something I'm also dealing with, so surely in general in the situation I'm interested in $\bar p$ may not be a pushforward of $p$. Btw, you shall know that one I guess.
Jan
14
accepted Existence of a map connecting two marginals of a product measure
Jan
14
comment Existence of a map connecting two marginals of a product measure
@NateEldredge: Thanks. Nope, your example applies - you can post it as an answer (unless the question will be closed before that as a trivial one)
Jan
14
asked Existence of a map connecting two marginals of a product measure
Jan
2
comment Convex hulls of families of probability measures
Thanks, the second paper seems to provide interesting results regarding the connections between barycentric convexity and other types of convexity.
Jan
1
comment Convex hulls of families of probability measures
@D.Kelleher: sorry, I misread your previous comment - now I understand what you meant, thanks for clarifying. The idempotence of $\operatorname{sco}$ holds at least for analytic sets (see my answer below).
Jan
1
answered Convex hulls of families of probability measures
Jan
1
comment Convex hulls of families of probability measures
@D.Kelleher: I see, could you clarify where the assumption of the idempotence of $\operatorname{sco}$ is used in Choquet's theorem? I don't see it is mentioned in the formulation of the result.
Dec
28
comment Convex hulls of families of probability measures
@D.Kelleher: can you suggest any sufficient conditions for the idempotence of $\operatorname{sco}$? Also, the Choquet's theorem you are talking about can be found in "Lecture notes on" I guess, isn't it?
Dec
28
comment Convex hulls of families of probability measures
Thanks, Gerald - I'll look into this. Do you know how can I find the second paper?
Dec
27
comment Convex hulls of families of probability measures
@MichaelGreinecker: by a convex combination I mean the integral over a "weighting" measure $\nu$ which gives a full outer measure to $P$ (at least I'm not aware of any other definition to be used here). Can you say that $\operatorname{sco}$ is idempotent?
Dec
27
revised Convex hulls of families of probability measures
added 210 characters in body