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作者：GLOVER, J
摘要：The symmetry groups of the potential theory of a Markov process X(t) are used to introduce new algebraic and topological structures on the state space and the process. For example, let G be the collection of bijections phi on E which preserve the collection of excessive functions. Assume there is a transitive subgroup H of the symmetry group G such that the only map phi-epsilon-H fixing a point e epsilon-E is the identity map on E. There is a bijection PSI: E --> H so that the algebraic struct...
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作者：FUNAKI, T; HANDA, K; UCHIYAMA, K
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：Hydrodynamic behavior of one-dimensional homogeneous exclusion processes with speed change on periodic lattices Z/NZ, N = 1,2,3,..., is studied. For every reversible exclusion process with nearest neighbor jumps and local interactions of gradient type it is shown that under diffusion-type scaling in space and time the empirical density fields of the processes converge to a weak solution of a nonlinear diffusion equation as N goes to infinity. Two classes of examples of exclusion processes as s...
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作者：SAMORODNITSKY, G; TAQQU, MS
作者单位：Boston University
摘要：We show that if X = (X1,..., X(d)) is a vector in R(d) and all linear combinations SIGMA-i = 1(d)C(i)X(i) are 1-stable random variables, then X is itself 1-stable. More generally, a probability measure-mu on a vector space whose univariate marginals are 1-stable is itself 1-stable. This settles an outstanding problem of Dudley and Kanter.
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作者：COSTANTINI, C
摘要：Consider a stochastic process consisting of the pair of a position and a velocity, in a piecewise l1 d-dimensional domain. In the interior of the domain the dynamics are assigned by a potential and by random changes of the velocity occurring at exponentially distributed times, according to a probability distribution which may depend on the current position and velocity. On the boundary the process reflects physically (the angle of reflection equals the angle of incidence). First it is shown th...
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作者：SHOR, PW; YUKICH, JE
作者单位：Lehigh University
摘要：In this article we solve the minimax grid matching problem in dimensions greater than two. As a by-product, we settle a long-open problem involving the Glivenko-Cantelli convergence of empirical measures.
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作者：WANG, YH
摘要：In 1971, Simons and Johnson showed that the classical theorem of binomial to Poisson convergence is actually stronger than in the usual sense. Their result was proved valid also for the distributions of sums of independent, but not necessarily identically distributed, Bernoulli random variables by Chen in 1974. Here we show that their result is indeed true for a much larger class of random variables. The limiting distribution is generalized to a compound Poisson distribution.
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作者：GANG, W
摘要：Let f be a real martingale and s(f) its conditional square function. Then the following inequalities are sharp: parallel-to f parallel-to p less-than-or-equal-to square-root 2/p parallel-to s(f) parallel-to p, 0 < p less-than-or-equal-to 2, square-root 2/p parallel-to s(f) parallel-to p less-than-or-equal-to parallel-to f parallel-to p, p greater-than-or-equal-to 2. The second inequality is still sharp if f is replaced by the maximal function f*. Let S(f) denote the square function of f. Then ...
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作者：LEGALL, JF
摘要：We propose a trajectorial construction of a class of measure-valued Markov processes, called superprocesses or measure-valued branching processes, which have been studied extensively in the last few years. These processes were originally defined as weak limits of systems of branching particles. The basic idea of our construction is to use the branching structure of excursions of a linear Brownian motion to model the branching mechanism of the superprocess. Without any additional effort, our ap...
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作者：YAGUCHI, H
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作者：SHORACK, GR
摘要：A huge body of if and only if theorems can be obtained based on certain strong embedding theorems for the partial sum process S(n) and the uniform empirical and quantile processes U(n) and V(n). This embedding was accomplished in 1986 by M. Csorgo, S. Csorgo, L. Horvath and D. Mason. Their embedding is beautifully formulated so that many necessary and sufficient type results can be established using it. It is worthwhile to have an accessible proof. Indeed, these authors have since produced two...
