Timeline for Regularity of random Fourier series
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2014 at 10:49 | comment | added | Liviu Nicolaescu | You can find a nice presentation of the regularity properties of Gaussian random fields in the Adler &Taylor monograph Random fields and geometry. | |
| Nov 3, 2014 at 19:31 | comment | added | Alexander Shamov | @IgorRivin: ... For Gaussians there is a well-developed theory that provides estimates based on the metric-entropy-like properties of the canonical metric on the parameter space, culminating in Talagrand's necessary and sufficient condition for boundedness/continuity. For a readable introduction see Adler's "An introduction to continuity, extrema, ...". There is also Talagrand's book "Generic chaining" on that, but I haven't really read it... | |
| Nov 3, 2014 at 19:29 | comment | added | Alexander Shamov | @IgorRivin: Well, Kolmogorov's criterion is classical, and you can find at least the one-dimensional version in any textbook that touches stochastic processes; in the $n$-dimensional case see, e.g., Theorem 2.23 in Kallenberg's "Foundations of Modern Probability". | |
| Nov 3, 2014 at 17:36 | vote | accept | Igor Rivin | ||
| Nov 3, 2014 at 14:55 | comment | added | Igor Rivin | Thanks! Is there some canonical reference for all this (Scheutzow's survey is quite nice, but assumes quite a bit...) | |
| Nov 2, 2014 at 23:28 | history | edited | Alexander Shamov | CC BY-SA 3.0 |
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| Nov 2, 2014 at 23:11 | history | edited | Alexander Shamov | CC BY-SA 3.0 |
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| Nov 2, 2014 at 23:01 | history | answered | Alexander Shamov | CC BY-SA 3.0 |