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作者：LALLEY, S; SELLKE, T
摘要：Let R(t) be the position of the rightmost particle at time t in a time-homogeneous one-dimensional branching diffusion process. Let gamma(alpha, t) be the alpha-th quantile of R(t) under P0, where P(x) denotes the probability measure of the branching diffusion process starting with a single particle at position x. We show that gamma(alpha, t) is a limiting quantile of R(t) under P(x) in the sense that lim(t-->infinity) P(x){R(t) less-than-or-equal-to gamma(alpha, t)} exists for all alpha is-an...
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作者：ALGOET, P
作者单位：Stanford University
摘要：We discuss universal schemes for portfolio selection. When such a scheme is used for investment in a stationary ergodic market with unknown distribution, the compounded capital will grow with the same limiting rate as could be achieved if the infinite past and hence of the distribution of the market were known to begin with. By specializing the market to a Kelly horse race, we obtain a universal scheme for gambling on a stationary ergodic process with values in a finite set. We point out the c...
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作者：DONNELLY, P; JOYCE, P
作者单位：University of Idaho; University of Southern California
摘要：The population genealogical processes associated with a wide range of exchangeable reproductive models (including the Wright-Fisher model) are shown to converge weakly, as the population size becomes large, to a particularly tractable limiting process, the age-ordered analog of Kingman's coalescent. This result extends the known convergence results for sample processes and effectively completes the robustness theory for neutral genealogies. Its consequences, which include a unification of the ...
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作者：SCHONMANN, RH
作者单位：Universidade de Sao Paulo
摘要：We consider some deterministic cellular automata on the state space {0, 1}L(d) evolving in discrete time, starting from product measures. Basic features of the dynamics include: 1's do not change, translation invariance, attractiveness and nearest neighbor interaction. The class of models which is studied generalizes the bootstrap percolation rules, in which a 0 changes to a 1 when it has at least l neighbors which are 1. Our main concern is with critical phenomena occurring with these models....
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作者：TRIBE, R
摘要：In this paper we use a martingale problem characterization to study the behavior of finite measure valued superprocesses with a variety of spatial motions. In general the superprocess, when normalized to be a probability, will converge to a point mass at its extinction time. For some spatial motions we prove that there are times near extinction at which the closed support of the process is concentrated near one point. We obtain a Tanaka formula for the measure of a half space under a one dimen...
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作者：MARCUS, MB; ROSEN, J
作者单位：Texas A&M University System; Texas A&M University College Station; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let {L(t)x, (t, x) is-an-element-of R+ X T} be the local time of a real-valued symmetric stable process of order 1 < beta less-than-or-equal-to 2 and let {pi(n)} be a sequence of partitions of [0, a]. Results are obtained for [GRAPHICS] both almost surely and in L(r) for all r > 0. Results are also obtained for a similar expression but where the supremum of the sum is taken over all partitions of [0, a] and a function other than a power is applied to the increments of the local times. The proo...
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作者：BACCELLI, F; LIU, Z
摘要：This paper is concerned with a class of stochastic recursive sequences that arise in various branches of queueing theory. First, we make use of Kingman's subadditive ergodic theorem to determine the stability region of this type of sequence, or equivalently, the condition under which they converge weakly to a finite limit. Under this stability condition, we also show that these sequences admit a unique finite stationary regime and that regardless of the initial condition, the transient sequenc...
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作者：SHEEHY, A; WELLNER, JA
作者单位：University of Washington; University of Washington Seattle
摘要：A class F of measurable functions on a probability space (A, A, P) is called a P-Donsker class and we also write F is-an-element-of CLT(P), if the empirical processes X(n)P = square-root n (P(n) - P) converge weakly to a P-Brownian bridge G(P) having bounded uniformly continuous sample paths almost surely. If this convergence holds for every probability measure P on (A, A), then F is called a universal Donsker class and we write F is-an-element-of CLT(M), where M = {all probability measures on...
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作者：EINMAHL, JHJ
摘要：The tail empirical process is defined to be for each n is-an-element-of N, w(n)(t) = (n/k(n))1/2-alpha(n)(tk(n)/n), 0 less-than-or-equal-to t less-than-or-equal-to 1, where alpha(n) is the empirical process based on the first n of a sequence of independent uniform (0, 1) random variables and {k(n)}n=1infinity is a sequence of positive numbers with k(n)/n --> 0 and k(n) --> infinity. In this paper a complete description of the almost sure behavior of the weighted empirical process alpha(n)alpha...
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作者：PITTEL, B
