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作者：Le Jan, Y; Raimond, O
作者单位：Universite Paris Saclay
摘要：This paper gives a construction of sticky flows on the circle. Sticky flows give examples of stochastic flows of kernels that interpolates between Arratia's coalescing flow and the deterministic diffusion flow. They are associated with systems of sticky independent Brownian particles on the circle, for some fixed parameter of stickyness. It is proved that the noise generated by Brownian sticky flows is black. A new proof of the fact that the noise of Arratia's coalescing flow is black is given.
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作者：Giné, E; Koltchinskii, V; Sakhanenko, L
作者单位：University of Connecticut; University of Connecticut; University of New Mexico; Michigan State University
摘要：Let f(n) denote a kernel density estimator of a bounded continuous density f in the real line. Let Psi(t) be a positive continuous function such that parallel toPsif(beta)parallel to(infinity) < infinity. Under natural smoothness conditions, necessary and sufficient conditions for the sequence root nh(n)/2log(n)(h-1) sup(tis an element ofR)\Psi(t)(f(n)(t) - Ef(n)(t))\(properly centered and normalized) to converge in distribution to the double exponential law are obtained. The proof is based on...
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作者：Wu, TJ; Tsai, MH
作者单位：National Cheng Kung University
摘要：Based on a random sample of size n from an unknown d-dimensional density f, the problem of selecting the bandwidths in kernel estimation of f is investigated. The optimal root n relative convergence rate for bandwidth selection is established and the information bounds in this convergence are given, and a stabilized bandwidth selector (SBS) is proposed. It is known that for all d the bandwidths selected by the least squares cross-validation (LSCV) have large sample variations. The proposed SBS...
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作者：Abraham, R; Delmas, JF
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We consider a Brownian snake (W-s, s greater than or equal to 0) with underlying process a reflected Brownian motion in a bounded domain D. We construct a continuous additive functional (L-s, s greater than or equal to0) of the Brownian snake which counts the time spent by the end points (W) over cap (s) of the Brownian snake paths on partial derivativeD. The random measure Z = integraldelta(delta) over cap (s) dL(s) is supported by partial derivativeD. Then we represent the solution v of Delt...
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作者：Chen, ZQ; Kim, P
作者单位：University of Washington; University of Washington Seattle
摘要：Recently the authors showed that the Martin boundary and the minimal Martin boundary for a censored (or resurrected) alpha-stable process Y in a bounded C-1,C-1-open set D with alpha is an element of (1, 2 can all be identified with the Euclidean boundary D of D. Under the gaugeability assumption, we show that the Martin boundary and the minimal Martin boundary for the Schrodinger operator obtained from Y through a non-local Feynman-Kac transform can all be identified with partial derivativeD....
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作者：Zambotti, L
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
摘要：We consider a delphi interface model on a one-dimensional lattice with repulsion from a hard wall. We suppose that the repulsion is of the form cphi(-alpha-1), where c,alpha>0 and phi denotes the height of the interface from the wall. We prove convergence of the equilibrium fluctuations around the hydrodynamic limit to the solution of a SPDE with singular drift. If c-->0 the system becomes the Funaki-Olla delphi interface model with reflection at the wall, whose equilibrium fluctuations conver...
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作者：Klemelä, J; Tsybakov, AB
作者单位：Ruprecht Karls University Heidelberg; Universite Paris Cite; Sorbonne Universite
摘要：We consider nonparametric estimation of a multivariate function and its partial derivatives at a fixed point when the Riesz transform of the function is observed in Gaussian white noise. We assume that the unknown function belongs to some Sobolev class and construct an estimation procedure which achieves the best asymptotic minimax risk when the smoothness of the function is unknown.
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作者：Eichelsbacher, P; Löwe, M
作者单位：Ruhr University Bochum; University of Munster
摘要：We derive moderate deviation principles for the overlap parameter in the Hopfield model of spin glasses and neural networks. If the inverse temperature beta is different from the critical inverse temperature beta(c)=1 and the number of patterns M(N) satisfies M(N)/N --> 0, the overlap parameter multiplied by N-gamma, 1/2 < gamma < 1, obeys a moderate deviation principle with speed N1-2gamma and a quadratic rate function (i.e. the Gaussian limit for gamma = 1/2 remains visible on the moderate d...
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作者：Donati-Martin, C; Rouault, A; Yor, M; Zani, M
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：Let (X-t((delta)),tgreater than or equal to0) be the BESQ(delta) process starting at deltax. We are interested in large deviations as delta --> infinity for the family {delta(-1)X(t)((delta)), tless than or equal toT}(delta), - or, more generally, for the family of squared radial OUdelta process. The main properties of this family allow us to develop three different approaches: an exponential martingale method, a Cramer-type theorem, thanks to a remarkable additivity property, and a Wentzell-F...
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作者：Bertail, P; Clémençon, S
作者单位：Japan Science & Technology Agency (JST); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Nanterre; Sorbonne Universite; Universite Paris Cite
摘要：This paper is devoted to the problem of estimating functionals of type mu( f) = integral fd mu from observations drawn from a positive recurrent atomic Markov chain X = (X-n)(nis an element ofN) with stationary distribution mu. The properties of different estimators are studied. Beyond an accurate estimation of their bias, the estimation of their asymptotic variance is considered. We also show that the results of Malinovskii (1987) on the validity of the formal Edgeworth expansion for sample m...
