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This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the...
We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, for example, that sup...
We consider an efficient estimation of an unknown parameter appearing in both the drift and the diffusion coefficient for a d-dimensional dynamical system with small noise. Asymptotic properties of an...
This paper proposes an estimator of the correlation dimension of the skeleton for chaotic dynamical system with dynamic noise and prove the consistency of the estimator under some assumptions.
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam...
Higher Criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, Higher Criticism also has reasonable per...
The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a mathematically justifiable, computationally simple,...
We consider the problem of detecting edges in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the “smoot...
In a convolution model, we observe random variables whose distribution is the convolution of some unknown density f and some known or partially known noise density g. In this paper, we focus on stat...

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