bio | website | |
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location | Rehovot, Israel | |
age | 24 | |
visits | member for | 2 years, 7 months |
seen | 11 hours ago | |
stats | profile views | 701 |
I'm a PhD student in Weizmann Institute, specializing in Probability.
Nov 21 |
comment |
What is the best reference for Spectral theory?
Rudin's book gives a great background on functional analysis in general, including the spectral theorem and some very basic notions related to Banach algebras, but it I wouldn't say it touches any "true" spectral theory. It's merely a prerequisite. |
Nov 13 |
revised |
Is an infinite-dimensional “Lebesgue measure” uniquely determined by a set of positive finite measure?
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Nov 13 |
revised |
Is an infinite-dimensional “Lebesgue measure” uniquely determined by a set of positive finite measure?
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Nov 13 |
asked | Is an infinite-dimensional “Lebesgue measure” uniquely determined by a set of positive finite measure? |
Nov 6 |
awarded | Enthusiast |
Nov 3 |
comment |
Regularity of random Fourier series
@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 |
comment |
Regularity of random Fourier series
@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 |
comment |
Regularity of random Fourier series
@IgorRivin: I would rather say speculate that this "middle" is a manifestation of independence of coefficients - positive or negative correlation of, say, polynomial decay should probably give different regularity exponents. But I haven't done the exercise, so I don't know really... |
Nov 2 |
revised |
Regularity of random Fourier series
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Nov 2 |
revised |
Regularity of random Fourier series
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Nov 2 |
comment |
Regularity of random Fourier series
@YemonChoi: There is chapter on that in Kahane's book "Random series of functions". For the probabilistic sense of "random", of course. :) |
Nov 2 |
answered | Regularity of random Fourier series |
Sep 30 |
awarded | Explainer |
Sep 27 |
revised |
“Bad” lower functions for a Bessel process?
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Sep 27 |
asked | “Bad” lower functions for a Bessel process? |
Sep 25 |
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Derive concentration bound for the derivative
Why on Earth would you expect this for general $f$, given that the derivative may not even exist? |
Sep 24 |
awarded | Autobiographer |
Sep 24 |
comment |
Is it true that all stationary measurable stochastic processes are “measurably stationary”?
Of course you can. But the idea is pretty much standard anyway... |
Sep 23 |
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Is it true that all stationary measurable stochastic processes are “measurably stationary”?
There is indeed such a map, under the assumptions that a) $X$ generates the whole σ-algebra on $\Omega$, b) $(\Omega,\mathcal{F},\mathsf{P})$ is standard (see the references in en.wikipedia.org/wiki/…). But we don't actually need it. Please see the updated answer... |
Sep 23 |
revised |
Is it true that all stationary measurable stochastic processes are “measurably stationary”?
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