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seen Jan 16 '12 at 4:20

Dec
13
comment Stopping time of a Markov chain
I am not an expert, but wanted to point out that there is a 'standard' technique for approximating Markov chains by ODE's. One important name is Kurtz's theorem. The survey article "Differential equation approximations for Markov chains " by Richard W.R. Darling and James Ritchie Norris in Probability Surveys gives a good introduction, with a few examples about how to account for exit time approximations. One difficulty is that your increments are in theory quite large, even after rescaling. Truncating the step sizes at e.g. $\sqrt{n \log(n)}$ could resolve this problem.
Dec
13
comment Linear relations with small coefficients
The hypergraph picture seems right, though the problem originally posed doesn't have one. This process comes from bounding the probability of a large deviation for a martingale; it turns out that the typical error size is at most $O(M + \log(\sum_{i} c_{i}^{2}))$ with high probability. The original problem involves perturbing an $n$ by $n$ matrix with these $v[a,b,c,d]$ terms, which really is where they come from; this is an effort to understand some cancellation that might happen. The perturbations are very dependent, and this was the most promising estimate I could find based on simulation.
Dec
12
asked Linear relations with small coefficients
Nov
17
awarded  Scholar
Nov
17
accepted Stable Law with Rates
Nov
7
awarded  Editor
Nov
7
comment Stable Law with Rates
Also, I just realized I was being a little rude there with the edit - I think my initial question was quite unclear, with one mention of iid and then another mention of a mixing rate. Perhaps the new version is better.
Nov
7
comment Stable Law with Rates
Hello Igor, thank you for the response - the paper is quite interesting (and the application is even somewhat related to what I was thinking of studying). I think that you are studying the iid case, rather than the mixing case. On the other hand, the rates are much better than I would have expected. I may try to use the calculations anyway...
Nov
7
revised Stable Law with Rates
added 112 characters in body
Nov
5
awarded  Student
Nov
5
asked Stable Law with Rates