1,872 reputation
518
bio website
location Rehovot, Israel
age 24
visits member for 2 years, 7 months
seen 11 hours ago

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?
deleted 5 characters in body
Nov
13
revised Is an infinite-dimensional “Lebesgue measure” uniquely determined by a set of positive finite measure?
edited tags; added 1 character in body
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
added 2 characters in body
Nov
2
revised Regularity of random Fourier series
added 39 characters in body
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?
edited body
Sep
27
asked “Bad” lower functions for a Bessel process?
Sep
25
comment 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
comment 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”?
added 134 characters in body