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On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise
Coalesce duality entrance law Fisher-Wright noise particle system
2009/4/24
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...
On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise
Duality Brownian Particles Heat Equation Fisher-Wright Noise
2009/4/7
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...
A data-driven block thresholding approach to wavelet estimation
Adaptivity Besov body block thresholding James–Stein estimator nonparametric regression Stein’s unbiased risk estimate
2010/3/19
A data-driven block thresholding procedure for wavelet regression
is proposed and its theoretical and numerical properties are investigated.
The procedure empirically chooses the block size and thre...
Local superefficiency of data-driven projection density estimators in continuous time
Density estimation data-driven superefficiency continuous time processes
2009/2/23
We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F0 of densities that is dense in the family of all possibl...
Data-driven efficient score tests for deconvolution problems
Hypothesis testing statistical inverse problems deconvolution efficient score test model selection data-driven test
2010/4/30
We consider testing statistical hypotheses about densities of
signals in deconvolution models. A new approach to this problem is proposed.
We constructed score tests for the deconvolution with the k...
Asymptotics for Duration-Driven Long Range Dependent Processes
Long Memory Heavy Tails Sample Autocovariances Discrete Fourier Transform
2010/4/29
We consider processes with second order long range dependence resulting from heavy
tailed durations. We refer to this phenomenon as duration-driven long range dependence
(DDLRD), as opposed to the m...