Results 241 to 250 of about 382,423 (270)

Phase retrieval without small-ball probability assumptions: Stability and uniqueness

2015 International Conference on Sampling Theory and Applications (SampTA), 2015
We study stability and uniqueness for the phase retrieval problem. That is, we ask when is a signal x e Rn stably and uniquely determined (up to small perturbations), when one performs phaseless measurements of the form y i = |aT i x|2 (for i = 1,…, N), where the vectors a i e Rn are chosen independently at random, with each coordinate a ij e R ...
Felix Krahmer, Yi-Kai Liu
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Phase retrieval without small-ball probability assumptions: Recovery guarantees for phaselift

2015 International Conference on Sampling Theory and Applications (SampTA), 2015
We study the problem of recovering an unknown vector x e Rn from measurements of the form y i = |aT i x|2 (for i = 1,…, m), where the vectors a i e Rn are chosen independently at random, with each coordinate a ij e R being chosen independently from a fixed sub-Gaussian distribution D.
Felix Krahmer, Yi-Kai Liu
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Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

Journal of Theoretical Probability, 2000
Given a stochastic process \(X=(X(t))_{t\in T}\) over an index set \(T\) which is a.s.~bounded, the small ball problem for \(X\) (in the log-level) is to determine the behaviour of \(-\log(\sup_{t\in T}|X(t)|
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Small Ball Probabilities for a Centered Poisson Process of High Intensity

Journal of Mathematical Sciences, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some small ball probabilities for Gaussian processes under nonuniform norms

Journal of Theoretical Probability, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Small Ball Probability for the Stochastic Parabolic Equations

Fluctuation and Noise Letters
This paper is concerned with the small ball probability for the stochastic parabolic equations. By using comparison principle and the properties of Brownian motion, the small ball probability estimates of parabolic equations with Brownian motion are considered. Some new results are given.
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An asymptotic factorization of the Small–Ball Probability: theory and estimates

2017
This work reviews recent results on an asymptotic factorization of the Small–Ball Probability of a \( {\fancyscript{L}}_{[0,1]}^{2} \)–valued process, as the radius of the ball tends to zero. This factorization involves a volumetric term, a pseudo–density for the probability law of the process, and a correction factor.
Aubin, Jean Baptiste, BONGIORNO, Enea Giuseppe, GOIA, Aldo   +2 more
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Small Ball Probabilities Around Random Centers of Gaussian Measures and Applications to Quantization

Journal of Theoretical Probability, 2003
Let \(\mu\) be a centered Gaussian measure on a separable Hilbert space \((E,||\cdot||)\), \(X\) be a \(\mu\)-distributed random variable in \(E\), denote by \(\{\lambda_j\}\) the non-increasing sequence of eigenvalues of the covariance operator of \(\mu\) and let \(\{e_j\}\) be a corresponding basis of orthonormal eigenfunctions.
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High resolution coding of stochastic processes and small ball probabilities

2003
This thesis is concerned with the high resolution coding problem for Gaussian measures on Banach spaces. New relations between the asymptotics of small ball probabilities and the latter problem are derived. In the case where the underlying space is even a Hilbert space, the problem is solved explicitly under weak assumptions on the eigenvalues of the ...
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Ball milling-assisted preparation of N-doped biochar loaded with ferrous sulfide as persulfate activator for phenol degradation: Multiple active sites-triggered radical/non-radical mechanism

Applied Catalysis B: Environmental, 2022
Ying Zhang
exaly