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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...
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作者：Gamarnik, D
作者单位：International Business Machines (IBM); IBM USA
摘要：Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and a constraint is chosen from also uniformly at random. This procedure is repeated m times independently. We are interested in whether the resulting linear programming problem is feasible. We prove that the feasibility property experiences a linear phase transi...
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作者：Dzhaparidze, K; van Zanten, H
作者单位：Vrije Universiteit Amsterdam
摘要：Let B be a fractional Brownian motion with Hurst index His an element of(0,1). Denote by x(1)<... the positive, real zeros of the Bessel function J(-H) of the first kind of order -H, and let y(1),y(2)<... be the positive zeros of J(1-H). In this paper we prove the series representation [GRAPHICS] where X-1,X-2,... and Y-1,Y-2,... are independent, Gaussian random variables with mean zero and VarX(n)=2c(H)(2)x(n)(-2H)J(1-H)(-2)(x(n)), VarY(n)=2c(H)(2)y(n)(-2H)J(-H)(-2)(y(n)), and the constant c(...
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作者：Nazarov, AL; Nikitin, YY
作者单位：Saint Petersburg State University
摘要：We find the exact small deviation asymptotics for the L-2-norm of various m- times integrated Gaussian processes closely connected with the Wiener process and the Ornstein - Uhlenbeck process. Using a general approach from the spectral theory of linear differential operators we obtain the two-term spectral asymptotics of eigenvalues in corresponding boundary value problems. This enables us to improve the recent results from [15] on the small ball asymptotics for a class of m-times integrated W...
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作者：Yoshida, N
作者单位：University of Tokyo
摘要：Introducing a conditional mixing property, Gotze and Hipp's theory is generalized to a continuous-time conditional epsilon-Markov process satisfying this property. The Malliavin calculus for jump processes applies to random-coefficient stochastic differential equations with jumps with the aid of the support theorem to verify the non-degeneracy condition, i.e., a conditional type Cramer condition.
