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作者：ARRATIA, R; STARK, D; TAVARE, S
摘要：Assemblies are the decomposable combinatorial constructions characterized by the exponential formula for generating functions: Sigma p(n)s(n)/n! = exp(Sigma m(i)s(i)/i!). Here p(n) is the total number of constructions that can be formed from a set of size n, and m(n) is the number of these structures consisting of a single component. Examples of assemblies include permutations, graphs, 2-regular graphs, forests of rooted or unrooted trees, set partitions and mappings of a set into itself. If a...
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作者：DAVIS, RA; HSING, TL
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Let {xi(j)} be a strictly stationary sequence of random variables with regularly varying tail probabilities. We consider, via point process methods, weak convergence of the partial sums, S-n = xi(1) + ... + xi(n), suitably normalized, when {xi(j)} satisfies a mild mixing condition. We first give a characterization of the limit point processes for the sequence of point processes N-n with mass at the points {xi(j)/a(n), j = 1,..., n}, where a(n) is the 1 - n(-1) quantile of the distribution of \...
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作者：ALGOET, PH
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作者：HAHN, MG; KLASS, MJ
作者单位：University of California System; University of California Berkeley; Tufts University
摘要：Let X(1),X(2),... be independent, mean zero, uniformly hounded random variables with S-n = X(1) +...+ X(n). Optimal criteria are determined on the length and location of an interval Gamma so that P(S-n epsilon Gamma) is proportional to (\Gamma\/root VarS(n)) boolean AND 1. The proof makes an unusual use of support considerations.
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作者：HAMMACK, W
摘要：We obtain a sharp probability bound on the maximal function of a strong subordinate of a bounded submartingale. An analogous inequality also holds for stochastic integrals in which the integrator is a bounded submartingale and the integrand is a bounded predictable process.
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作者：OVERBECK, L; ROCKNER, M; SCHMULAND, B
作者单位：University of Alberta
摘要：We study a class of (nonsymmetric) Dirichlet forms (E, D(E)) having a space of measures as state space E and derive some general results about them. We show that under certain conditions they ''generate'' diffusion processes M. In particular, if M is ergodic and (E, D(E)) is symmetric w.r.t. quasi-every starting point, the large deviations of the empirical distribution of M are governed by E. We apply all of this to construct Fleming-Viot processes with interactive selection and prove some res...
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作者：PEMANTLE, R; PERES, Y
作者单位：University of California System; University of California Berkeley
摘要：We study the behavior of random walk in random environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges of a tree Gamma are i.i.d. random variables whose logarithms have mean zero and finite variance. Then the resulting RWRE is transient if simple random walk on Gamma is transient, but not vice versa We obtain general transience criteria for such walks, which...
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作者：Grimmett, G
摘要：The random-cluster model is a generalization of percolation and ferromagnetic Potts models, due to Fortuin and Kasteleyn. Not only is the random-cluster model a worthwhile topic for study in its own right, but also it provides much information about phase transitions in the associated physical models. This paper serves two functions. First, we introduce and survey random-cluster measures from the probabilist's point of view, giving clear statements of some of the many open problems. Second, we...
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作者：Vanderbei, RJ
摘要：Let D be a compact, convex domain in d-dimensional Euclidean space and let f be a nonnegative real-valued function defined on D. The classical optimal stopping problem is to find a stopping time tau* that attains the supremum v(x) = sup(tau) E(x)f(B(tau)). Here, B is a d-dimensional Brownian motion with absorption on the boundary of D and the supremum is over all stopping times. It is well known that v is characterized as the smallest superharmonic majorant of f. In this paper, we modify this ...
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作者：LEFEVRE, C; UTEV, S
作者单位：Novosibirsk State University
摘要：A so-called generalized epidemic model is considered that describes the spread of an infectious disease of the SIR type with any specified distribution for the infectious period. The statistic under study is the number of susceptibles who ultimately survive the disease. In a pioneering paper, Daniels established for a particular case that when the population is large, this variable may have a Poisson-like behavior. This result was discussed later by several authors. In the present work, a nece...
