Probability Theory and Related Fields

最新文章

• BROWNIAN-MOTION IN A POISSONIAN POTENTIAL AI翻译
  作者：SZNITMAN, AS
  摘要：We study here a d-dimensional Brownian motion in a random potential V(.,omega) obtained as the sum of translations of a given fixed non negative shape function at the points of a Poisson cloud of constant intensity nu. We are interested in the large t behavior for typical cloud configurations, of the Brownian path in time t under the influence of the natural Feynman-Kac weight associated to V(.,omega). In particular, we show that the location at time t of the process tends to be concentrated n...
• BAXTER INEQUALITY AND CONVERGENCE OF FINITE PREDICTORS OF MULTIVARIATE STOCHASTIC-PROCESSES AI翻译
  作者：CHENG, R; POURAHMADI, M
  作者单位：Northern Illinois University
  摘要：We show that smoothness properties of a spectral density matrix and its optimal factor are closely related when the density satisfies the boundedness condition. This is crucial in proving multivariate generalizations of Baxter's inequality and obtaining rates of convergence of finite predictors. We rely on a technique of Lowdenslager and Rosenblum relating the optimal factor to the spectral density via Toeplitz operators.
• A SHARP TRANSITION FOR THE 2-DIMENSIONAL ISING PERCOLATION AI翻译
  作者：HIGUCHI, Y
  摘要：We show that the percolation transition for the two-dimensional Ising model is sharp. Namely, we show that for every reciprocal temperature beta > 0, there exists a critical value h(c)(beta) of external magnetic field h such that the following two statements hold. If h > h(c)(beta), then the percolation probability (i.e., the probability that the origin is in the infinite cluster of + spins) with respect to the Gibbs state mu(beta,h) for the parameter (beta,h) is positive. If h < h(c)(beta), t...
• THE NOVIKOV AND ENTROPY CONDITIONS OF MULTIDIMENSIONAL DIFFUSION-PROCESSES WITH SINGULAR DRIFT AI翻译
  作者：STUMMER, W
  作者单位：University of Zurich; University Zurich Hospital
  摘要：We consider multidimensional stochastic differential equations of the form [GRAPHICS] with arbitrary initial (probability) distribution mu on R(d), d greater than or equal to 1. The first aim of this paper is to give handy-to-verify analytic (i.e. non-stochastic) conditions for the existence of a weak solution of (1), where the drift b will be allowed to have singularities. These investigations are illustrated by various examples. We first concentrate on (a uniform form of) the Novikov conditi...
• STABLE MIXED MOVING AVERAGES AI翻译
  作者：SURGAILIS, D; ROSINSKI, J; MANDREKAR, V; CAMBANIS, S
  作者单位：Vilnius University; University of Tennessee System; University of Tennessee Knoxville; Michigan State University
  摘要：The class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter function and the mixing measure, leading to a generalization of a theorem of Kanter (1973) for usual moving averages. Stable mixed moving averages contain sums of independent stable moving averages, are ergodic and are no...
• THE CENTRAL-LIMIT-THEOREM FOR THE INTERSECTION OF 2 INDEPENDENT WIENER SAUSAGES AI翻译
  作者：WEINRYB, S; YOR, M
  作者单位：Sorbonne Universite
  摘要：J.F. Le Gall [4] proved that n2 times the volume of the intersection of two independent Wiener sausages in R3 , with radius 1/n, converges in L2, as n --> infinity, towards a multiple of the intersection local time at 0, for the underlying Brownian motions. We complete this result by proving a corresponding central limit theorem.
• PERSISTENCE OF CRITICAL MULTITYPE PARTICLE AND MEASURE BRANCHING-PROCESSES AI翻译
  作者：GOROSTIZA, LG; ROELLY, S; WAKOLBINGER, A
  作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Johannes Kepler University Linz
  摘要：We consider a class of systems of particles of k types in R(d) undergoing spatiai diffusion and critical multitype branching, where the diffusions, the particle lifetimes and the branching laws depend on the types. We prove persistence criteria for such systems and for their corresponding high density limits known as multitype Dawson-Watanabe processes. The main tool is a representation of the Palm distributions for a general class of inhomogeneous critical branching particle systems, construc...
• SIZE-BIASED SAMPLING OF POISSON POINT-PROCESSES AND EXCURSIONS AI翻译
  作者：PERMAN, M; PITMAN, J; YOR, M
  作者单位：Sorbonne Universite; University of California System; University of California Berkeley
  摘要：Some general formulae are obtained for size-biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function. These formulae explain why in certain cases (gamma and stable) the size-biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking (residual allocation) scheme defined by independent beta random variables. An application is made to length biased sampling of excursion...
• ASYMPTOTIC EXPANSIONS OF MAXIMUM-LIKELIHOOD ESTIMATORS FOR SMALL DIFFUSIONS VIA THE THEORY OF MALLIAVIN WATANABE AI翻译
  作者：YOSHIDA, N
  摘要：The asymptotic expansions of the probability distributions of statistics for the small diffusion are derived by means of the Malliavin calculus. From this the second order efficiency of the maximum likelihood estimator is proved.
• SMOOTHED CROSS-VALIDATION AI翻译
  作者：HALL, P; MARRON, JS; PARK, BU
  作者单位：Seoul National University (SNU)
  摘要：For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be be...