-
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.
-
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...
-
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.
-
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.
-
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 ...
-
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...
-
作者：YAGUCHI, H
-
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...
-
作者：DUPUIS, P; ELLIS, RS; WEISS, A
作者单位：Nokia Corporation; Nokia Bell Labs; AT&T
摘要：In this paper we prove an upper large deviation bound for a general class of Markov processes, which includes processes with discontinuous statistics. We also specialize the results to a class of jump Markov processes that model scaled queueing systems.
-
作者：DYNKIN, EB
摘要：We start from a model of a branching particle system with immigration and with death rate and branching mechanism depending on time and location. Then we consider a limit case when the mass of particles and their life times are small and their density is high. This way, we construct a measure-valued process X(t) which we call a superprocess. Replacing the underlying Markov process xi-t by the corresponding historical process xi less-than-or-equal-to t, we construct a measure-valued process M(t...
