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作者：MAULDIN, RD; VONWEIZSACKER, H
作者单位：University of Kaiserslautern
摘要：It is shown that a perturbed Bernoulli probability transition kernel yields an explicit example of an orthogonality preserving kernel which is not completely orthogonal. In statistical language, such a kernel defines models P(theta), theta-epsilon [0, 1], in which there is no estimate that estimates theta perfectly for all theta, but there is, for any given prior distribution on theta and hypothesis H0 subset-of [0, 1], a perfect test for H0 against its complement [0, 1] / H0. It is also demon...
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作者：KURTZ, TG
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：An analog of conditions of Meyer and Zheng for the relative compactness (in the sense of convergence in distribution) of a sequence of stochastic processes is formulated for general separable metric spaces and the corresponding notion of convergence is characterized in terms of the convergence in the Skorohod topology of time changes of the original processes. In addition, convergence in distribution under the topology of convergence in measure is discussed and results of Jacod, Memin and Meti...
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作者：LINDVALL, T
摘要：We commemorate W. Doeblin with a brief recollection of his work, influence and life.
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作者：BERGER, E
摘要：In this paper we describe a general device that allows us to deduce various kinds of theorems (moment estimates, exponential inequalities, strong law of large numbers, stability results, bounded law of the iterated logarithm) for partial sums of independent vector-valued random variables from related results for partial sums of independent real-valued random variables. The concept of majorization will play a key role in our considerations.
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作者：CHAUVIN, B
摘要：For a branching Brownian motion, a probability space of trees is defined. By analogy with stopping times on R, stopping lines are defined to get a general branching property. We exhibit an intrinsic class of martingales which are products indexed by the elements of a stopping line. We prove that all these martingales have the same limit which we identify. Two particular cases arise: the line of particles living at time t and the first crossings of a straight line whose equation is y = at - x i...
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作者：BALDI, P
摘要：We consider a family of periodic diffusion processes in R(n) with homogenization and a small parameter multiplying the diffusion coefficient. We establish a large deviations principle and as an application we derive an interated logarithm law for periodic diffusions.
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作者：LEE, TY
摘要：A critical branching Brownian motion in R(d) is studied where the initial state is either a single particle or a homogeneous field with finite or infinite density. Conditioned on survival in a bounded subset B of R(d) at a large time t, some normalized limits of the number of particles in a bounded subset A are obtained. When the initial state is a single particle, the normalization factor is a power of t in low dimensions, a power of log t in the critical dimension and a constant in high dime...
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作者：GINE, E; ZINN, J
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Texas A&M University System; Texas A&M University College Station
摘要：It is proved that, for classes of functions F satisfying some measurability, the empirical processes indexed by F and based on P member-of P(S) satisfy the central limit theorem uniformly in P member-of P(S) if and only if the P-Brownian bridges G(P) indexed by F are sample bounded and rho-p uniformly continuous uniformly in P member-of P(S). Uniform exponential bounds for empirical processes indexed by universal bounded Donsker and uniform Donsker classes of functions are also obtained.
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作者：HALL, P
摘要：Laws of the iterated logarithm are derived for row sums of triangular arrays of independent random variables, in the context of nonparametric regression estimators. These laws provide exact strong convergence rates for kernel type nonparametric regression estimators. They apply to the important case where design points are conditioned upon, and permit the design to be multivariate. We impose minimal conditions on the error distribution; in fact, only finite variance is needed.
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作者：MOUNTFORD, TS; PORT, SC
摘要：It is shown that all Levy processes on the line whose paths are of bounded variation have a closed range over any finite time interval that is nowhere dense except for those processes having positive (negative) drift with Levy measure finite on (0, infinity) [finite on (-infinity, 0)].
