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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 $P$.