Ilya
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 Apr 28 comment Extreme couplings Thanks, I will take a look. Apr 28 comment Extreme couplings You are right, I'm used to think in terms of integrals. Apr 28 comment Extreme couplings Thanks, in your example - what if $M$ can be represented as a combination of some other elements w.r.t. general measure, not just finite linear combination? I highly doubt that, but unfortunately in that case we can't really easily use dominance, hence I am not sure how would you prove that. Apr 25 comment Generalized Ito's lemma What's a problem of finding derivative for intervals where $M$ is constant, and adding jumps as a separate sum? Apr 25 comment Non-existence for a sort of probability measures So what's the problem with existence of family, if its elements do exist? Apr 25 comment Non-existence for a sort of probability measures I don't really see why would you care about all $\theta$ at the same time here. Does $P_\theta$ exist for all/any non-zero $\theta$? Apr 22 answered Is there an easy way to convert a non-deterministic optimal policy to a deterministic optimal policy for a given MDP? Apr 21 revised Conditions for existence of dominating $\sigma$-finite measure for all conditional distributions made the title more clear Apr 21 comment Is there an easy way to convert a non-deterministic optimal policy to a deterministic optimal policy for a given MDP? Can't you just follow a greedy policy in this case? AFAIK, optimal non-deterministic policy is any probability measure on maximal set of the value function, so picking just any point there would suffice. Apr 21 comment Infinitesimal generator and stationarity What exactly does your "moreover" statement mean? Apr 21 comment Conditions for existence of dominating $\sigma$-finite measure for all conditional distributions One sufficient condition (even though trivial, perhaps) is that if $P \in Q$ and $P' \ll P$ then $P' \in Q$ Apr 21 suggested approved edit on Conditions for existence of dominating $\sigma$-finite measure for all conditional distributions Apr 21 answered Measurable $\epsilon$-optimal selection with an analytically measurable stochastic kernel Mar 3 comment Generalizations of the Birkhoff-von Neumann Theorem Can you provide a reference to the last sentence? Namely, what are the extreme points here. Related to this question Mar 3 comment Extreme couplings @michael: afaik in the discrete case there is going to be a finite number of extreme points, however no, I don't know how to describe them nicely. Mar 3 asked Extreme couplings Mar 3 accepted Convex hulls of families of probability measures Feb 25 comment Bounds on Wasserstein (Kantorovich) distance @FedorPetrov: a typo, $\lambda = \gamma$ Feb 25 revised Bounds on Wasserstein (Kantorovich) distance deleted 2 characters in body Feb 25 comment Bounds on Wasserstein (Kantorovich) distance @NateEldredge: added. True for the $\nu$, and $P$ is the joint distribution with the left marginal $\mu$ and conditional probability $P$.