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作者：GRIFFIN, PS; MCCONNELL, TR
摘要：Let T-r be the first time a sum S-n of nondegenerate i.i.d. random vectors in R(d) leaves the sphere of radius r in some given norm. We characterize, in terms of the distribution of the individual summands, the following probabilistic behavior: S-Tr/parallel to S(Tr)parallel to has no subsequential weak limit supported on a closed half-space. In one dimension, this result solves a very general form of the gambler's ruin problem. We also characterize the existence of degenerate limits and obtai...
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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider the product measure mu(p) on {0, 1}(n), when 0 (resp. 1) is given weight 1 - p (resp, p). Consider a monotone subset A of {0, 1}(n). We give a precise quantitative form to the following statement: if A does not depend much on any given coordinate, d mu(p)(A)/dp is large. Thus, in that case, there is a threshold effect and mu(p)(A) jumps from near 0 to near 1 in a small interval.
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作者：MAJOR, P
摘要：We prove limit theorems for weighted U-statistics and express the limit by means of multiple stochastic integrals. This is a generalization of the paper by O'Neil and Redner. In that paper the method of moments was applied which does not work in the general case. Hence we had to work out a different method. In particular, in Theorem 4 we describe the limit of a model proposed by O'Neil and Redner. In this model the weight functions cause an intricate cancellation, and the limit can be presente...
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作者：CHEN, HN
摘要：We continue our study on the stability properties of a population growth model with sexual reproduction on Z(d), d greater than or equal to 2. In the author's previous work, it was proved that in the type IV process (the two-dimensional symmetric model on Z(2)), the vacant state empty set is stable under perturbation of the initial state (the first kind of perturbation), and it is unstable under perturbation of the birth rate (the second kind of perturbation). In this paper we prove that in th...
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作者：BARTOSZEK, W
摘要：Let (xi n)(n greater than or equal to 0) be a random walk on a countable group G. Sufficient and necessary conditions for the existence of a finite set A subset of or equal to G and a sequence g(n) is an element of G such that for all natural n we have P(xi(n) is an element of A/xi(0) = g(n)) = 1 are presented. This provides a complete solution to the problem of behavior of concentration functions on discrete groups.
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作者：BEZUIDENHOUT, C; GRAY, L
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We study a class of attractive spin systems. We prove that for these processes the system dies out when the parameters are on the critical surface. We also prove that the supercritical process survives with positive probability in a sufficiently thick space-time ''slab.''
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作者：MADRAS, N; SCHINAZI, R; SCHONMANN, RH
作者单位：University of Colorado System; University of Colorado at Colorado Springs; University of California System; University of California Los Angeles
摘要：We consider the contact process with inhomogeneous deterministic death rates. We prove the following: 1. Such models may have discontinuous transitions, in the sense of surviving at the critical point. 2. If the death rates are identically 1, except on a set which is small enough in a proper sense and where the death rates take a fixed value smaller than 1, then the critical point is identical to that of the homogeneous system. Extensions of the results to other (d + 1)-dimensional systems wit...
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作者：KNIGHT, FB; MAISONNEUVE, B
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Let R be a random time in F-infinity, the terminal element of a filtration F-t satisfying the usual hypotheses. It is shown that if optional sampling holds at R for all bounded martingales, then R is optional. If F-t is the natural pseudo-path filtration of a measurable process X(t), then R is optional if (and only if) the conditional distribution of X(R+), given F-R is Z(R), where Z(t) is an optional version of the conditional distribution of X(t+), given F-t.
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作者：SLUD, EV
摘要：Let X = (X(t),t greater than or equal to 0) be a stationary Gaussian process with zero mean, continuous spectral distribution and twice-differentiable correlation function. An explicit representation is given for the number N-psi(T) of crossings of a C-1 curve psi by X on the bounded interval [0, T], in a multiple Wiener-It (o) over cap integral expansion. This continues work of the author in which the result was given for psi equivalent to 0. The representation is applied to prove new central...
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作者：SCHWEIZER, M
摘要：Let X be a semimartingale and Theta the space of all predictable X-integrable processes theta such that integral theta dX is in the space S-2 of semimartingales, we consider the problem of approximating a given random variable H epsilon L(2) by a stochastic integral integral(0)(T) theta(s) dX(s), with respect to the L(2)-norm. If X is special and has the form X = X(0) +M+ integral alpha d(M), we construct a solution in feedback form under the assumptions that integral alpha(2)d(M) is determini...
