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作者：Gao, F; Hannig, J; Torcaso, F
作者单位：University of Idaho; Colorado State University System; Colorado State University Fort Collins; Johns Hopkins University
摘要：We will introduce a class of m-times integrated Brownian motions. The exact asymptotic expansions for the L-2-small ball probabilities will be discussed for members of this class, of which the usual m-times integrated Brownian motion is an example. Another example will be what we call an Euler-integrated Brownian motion. We will also find very sharp estimates for the asymptotics of the eigenvalues of the covariance operator of integrated Brownian motions and will, therefore, obtain exact, not ...
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作者：Shirai, T; Takahashi, Y
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology; Kanazawa University; Kyoto University
摘要：We construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants. Under a mild condition they turn out unique Gibbs measures. Also some ergodic properties, including the entropy positivity, are discussed in the lattice case.
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作者：Guillin, A
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Consider the following stochastic differential equation in R-d: dX(t)(epsilon) = b(X-t(epsilon), xi(t/epsilon)) dt + rootepsilona(X-t(epsilon), xi(t/epsilon)) dW(t), X-0(epsilon) = X-0, where the random environment (xi(t)) is an exponentially ergodic Markov process, independent of the Wiener process (W-t), with invariant probability measure pi, and epsilon is some small parameter. In this paper we prove the moderate deviations for the averaging principle of X-epsilon, that is, deviations of (X...
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作者：Benjamini, I; Kalai, G; Schramm, O
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; Microsoft
摘要：Let 0 < a < b < infinity, and for each edge e of Z(d) let omega(e) = a or omega(e) = b, each with probability 1/2, independently. This induces a random metric dist(omega) on the vertices of Zd, called first passage percolation. We prove that for d > 1, the distance dist(omega)(0, v) from the origin to a vertex v, \v\ > 2, has variance bounded by C\v\/log \v\, where C = C(a, b, d) is a constant which may only depend on a, b and d. Some related variants are also discussed.
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作者：Mattner, L
作者单位：University of Lubeck
摘要：This is a contribution to the theory of sums of independent random variables at the level of optimal explicit inequalities: we compute the optimal constants in Hornich's lower bounds for the mean absolute deviations of sample means. This is done by reducing the original problem to the elementary one of determining the minimally concentrated binomial distributions B-n,B-p with fixed sample size parameter n.
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作者：Dzhaparidze, K; Spreij, P; Valkeila, E
作者单位：University of Amsterdam; University of Helsinki
摘要：In this paper we give explicit representations for Kullback-Leibler information numbers between a priori and a posteriori distributions, when the observations come from a semimartingale. We assume that the distribution of the observed sernimartingale is described in terms of the so-called triplet of predictable characteristics. We end by considering the corresponding notions in a model with a fractional noise.
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作者：Brofferio, S
作者单位：Graz University of Technology
摘要：The auto-regressive model on R-d defined by the recurrence equation Y-n(y) = a(n)Y(n-1)(y) + B-n, where {(a(n), B-n)}(n) is a sequence of i.i.d. random variables in R+* x R-d, has, in the r=critical case E[loga(1)] = 0, a local contraction property, that is, when Y-n(y) is in a compact set the distance \Y-n(y) - Y-n(x)\ converges almost surely to 0. We determine the speed of this convergence and we use this asymptotic estimate to deal with some higher-dimensional situations. In particular, we ...
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作者：Pardoux, É; Veretennikov, Y
作者单位：Aix-Marseille Universite; University of Leeds; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：Three different results are established which turn out to be closely connected so that the first one implies the second one which in turn implies the third one. The first one states the smoothness of an invariant diffusion density with respect to a parameter. The second establishes a similar smoothness of the solution of the Poisson equation in R-d. The third one states a diffusion approximation result, or in other words an averaging of singularly perturbed diffusion for fully coupled SDE syst...
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作者：Bruss, FT
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：The odds theorem gives a unified answer to a class of stopping problems on sequences of independent indicator functions. The success probability of the optimal rule is known to be larger than Re-R, where R defined in the theorem satisfies R greater than or equal to 1 in the more interesting case. The following findings strengthen this result by showing that 1/e is then a lower bound. Knowing that this is the best possible uniform lower bound motivates this addendum.
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作者：Bendikov, A; Saloff-Coste, L
作者单位：Cornell University
摘要：We study the regularity of the sample paths of certain Brownian motions on the infinite dimensional torus T-infinity and other compact connected groups in terms of the associated intrinsic distance. For each lambda is an element of (0, 1), we give examples where the intrinsic distance d is continuous and defines the topology of T-infinity and where the sample paths satisfy 0 < lim inf(t-->0) d(X-0,X-t)/t((1-lambda)/2) less than or equal to lim sup(t-->0) d(X-0,X-t)/t((1-lambda)/2) < infinity a...
