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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider two independent sequences (X(i))i less-than-or-equal-to n and (X(i)')i less-than-or-equal-to n that are independent and uniformly distributed over [0, 1]d, d greater-than-or-equal-to 3. Under mild regularity conditions, we describe the convex functions phi such that, with large probability, there exists a one-to-one map pi from {1, ..., n} to {1, ..., n} for which [GRAPHICS] where K(p) depends on phi only
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作者：VANDENBERG, J; MAES, C
摘要：Recently, one of the authors (van den Berg) has obtained a uniqueness condition for Gibbs measures, in terms of disagreement percolation involving two independent realizations. In the present paper we study the dependence of Markov fields on boundary conditions by taking a more suitable coupling. This coupling leads to a new uniqueness condition, which improves the one mentioned above. We also compare it with the Dobrushin uniqueness condition. In the case of the Ising model, our coupling shar...
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作者：XIANG, XJ
作者单位：University of Chicago
摘要：In this article we derive a law of the logarithm for the maximal deviation between two kernel-type quantile density estimators and the true underlying quantile density function in the randomly right-censored case. Extensions to higher derivatives are included. The results are applied to get optimal bandwidths with respect to almost sure uniform convergence.
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作者：SEPPALAINEN, T
摘要：This paper presents almost sure uniform large deviation principles for the empirical distributions and empirical processes of Markov chains with random transitions. The results are derived under assumptions that generalize assumptions earlier used for time-homogeneous chains. The rate functions for the skew chain are expressed in terms of the Donsker-Varadhan functional and relative entropy The sample chain rates are different, but they have natural upper and lower bounds in terms of familiar ...
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作者：KOURITZIN, MA; HEUNIS, AJ
作者单位：University of Waterloo
摘要：Consider the following random ordinary differential equation: X(epsilon)(tau) = F(X(epsilon)(tau), (tau/epsilon, omega) subject to X(epsilon)(0) = x0, where {F(x, t, omega), t > 0} are stochastic processes indexed by x in R(d), and the dependence on x is sufficiently regular to ensure that the equation has a unique solution X(epsilon)(tau, omega) over the interval 0 less-than-or-equal-to T less-than-or-equal-to 1 for each epsilon > 0. Under rather general conditions one can associate with the ...
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作者：WU, YD
摘要：In this paper we consider a multilevel branching diffusion particle system and its diffusion approximation, which can be characterized as an M(M(R(d)))-valued process. The long term behavior of the limiting process is studied. The main results are that if d less-than-or-equal-to 4, then the two level M(M(R(d)))-valued process suffers local extinction, and if d = 4, then the process has a self-similarity property.
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作者：BASS, RF; BURDZY, K; KHOSHNEVISAN, D
作者单位：Utah System of Higher Education; University of Utah
摘要：For each a is-an-element-of (0, 1/2), there exists a random measure beta(alpha) which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure beta(alpha) is carried by a set which has Hausdorff dimension equal to 2 - alpha. A Palm measure interpretation of beta(alpha) is given.
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作者：BOLTHAUSEN, E
摘要：We consider an ordinary, symmetric, continuous-time random walk on the two-dimensional lattice Z2. The distribution of the walk is transformed by a density which discounts exponentially the number of points visited up to time T. This introduces a self-attracting interaction of the paths. We study the asymptotic behavior for T --> infinity. It turns out that the displacement is asymptotically of order T1/4. The main technique for proving the result is a refined analysis of large deviation proba...
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作者：DUPUIS, P; WILLIAMS, RJ
作者单位：University of California System; University of California San Diego
摘要：We prove that a sufficient condition for a semimartingale reflecting Brownian motion in an orthant (SRBM) to be positive recurrent is that all solutions of an associated deterministic Skorokhod problem are attracted to the origin. To prove this result, we construct a Lyapunov function for the SRBM.
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作者：COX, JT; GREVEN, A
作者单位：University of Gottingen
摘要：Let x(t) = {x(i)(t), i is-an-element-to Z(d)} be the solution of the system of stochastic differential equations dx(i)(t) = (SIGMA(j is-an-element-of Z(d) a (i, j)x(j)(t) - x(i)(t)) dt + square-root 2g(x(i)(t)) dw(i)(t), i is-an-element-of Z(d). Here g: [0, 1] - R+ satisfies g > 0 on (0, 1), g(0) = g(1) = 0, g is Lipschitz, a(i,j) is an irreducible random walk kernel on Z(d) and {w(i)(t), i is-an-element-of Z(d)) is a family of standard, independent Brownian motions on R; x(t) is a Markov proc...
