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gregarki khayal's user avatar
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gregarki khayal
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The time when a quasi-linear hyperbolic system produces shocks
This exactly solves my question. Just as a reference, we can find similar argument (for a bit more general case) in Peter D. Lax's paper (Journal of Mathematical Physics 5, 1964).
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Local central limit theorem far from the center
Yes, I realized that it depends on the tail of X. I am typically interested in the case that X is sub-Gaussian: $Ee^{sX} < e^{cs^2}$ for all $s$.
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Local central limit theorem far from the center
We can do explicit calculation when X is Gaussian. So I want to know the case that X is subgaussian: $E [e^{sX}] < e^{c^2s^2/2}$ for any $s$ in $R$.
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The eigenfunctions of an operator commuting with all rotations.
It seems that I made a lot of mistakes in my question... I will try to edit it and accept the answer. Thank you very much.
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The (infinite) invariant measure of an SPDE
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