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作者：NORRIS, JR
摘要：The heat kernel and its derivatives of a vector Laplacian on the sections of a bundle over a compact Riemannian manifold are expressed as products of the scalar heat kernel of the manifold and path integrals over the Brownian bridge. The small-time asymptotics of these integrals are computed.
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作者：EINMAHL, U; MASON, DM
作者单位：University of Delaware
摘要：We provide a detailed description of the rate of clustering in Strassen's functional law of the iterated logarithm for partial sum processes. Necessary and sufficient conditions are given for certain clustering rates in terms of moment-type conditions. In the process, we also derive a new strong approximation of sums of iid random variables by a Wiener process.
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作者：IVANOFF, BG; MERZBACH, E; SCHIOPUKRATINA, I
作者单位：Bar Ilan University
摘要：As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable sigma-algebra in terms of adapted and ''left-continuous'' processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable sigma-algebra can be ...
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作者：PATZSCHKE, N; ZAHLE, M
摘要：In an earlier paper Patzschke and U. Zahle [11] have proved the existence of a fractional tangent measure at the typical point of a self-similar random measure Phi under rather special technical assumptions. In the present paper we remove the most restrictive one. Here we suppose the open set condition for the similarities, a constant positive lower bound for the random contraction ratios, and vanishing Phi on the boundary of the open set with probability 1. The tangent measure is D-scale-inva...
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作者：BERLINET, A
摘要：Recent literature on functional estimation has shown the importance of kernels with vanishing moments although no general framework was given to build kernels of increasing order apart from some specific methods based on moment relationships. The purpose of the present paper is to develop such a framework and to show how to build higher order kernels with nice properties and to solve optimization problems about kernels. The proofs given here, unlike standard variational arguments, explain why ...
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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...
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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...
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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...
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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...
