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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 |