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作者：SAMUELCAHN, E
摘要：Let X(i) be i.i.d. random variables, 0 less-than-or-equal-to X(i) less-than-or-equal-to 1 and c greater-than-or-equal-to 0, and let Y(i) = X(i) - ic. It is shown that for all n, all c and all such X(i), E(max(i greater-than-or-equal-to 1 Y(i)) - sup(t) EY(t) < e-1, where t is a stopping rule and e-1 is shown to be the best bound for which the inequality holds. Specific bounds are also obtained for fixed n or fixed c. These results are very similar to those obtained by Jones for a similar probl...
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作者：AVRAM, F; TAQQU, MS
作者单位：Boston University; University of North Carolina; University of North Carolina Chapel Hill
摘要：Skorohod has shown that the convergence of sums of i.i.d. random variables to an alpha-stable Levy motion, with 0 < alpha < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving averages with at least two nonzero coefficients, weak-J1 convergence cannot hold because adjacent jumps of the process can coalesce in the limit; however, if the moving average coefficients are positive, then the adjacent jumps are essentially monotone and one can hav...
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作者：BACCELLI, F
摘要：Stochastic Petri networks provide a general formalism for describing the dynamics of discrete event systems. The present paper focuses on a subclass of stochastic Petri networks called stochastic event graphs, under the assumption that the variables used for their timing form stationary and ergodic sequences of random variables. We show that such stochastic event graphs can be seen as a (max, +) linear system in a random, stationary and ergodic environment. We then analyze the associated Lyapo...
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作者：SHIELDS, PC
作者单位：Eotvos Lorand University
摘要：Grassberger suggested an interesting entropy estimator, namely, n log n/SIGMA(i = 1)nL(i)n, where L(i)n is the shortest prefix of x(i), x(i + 1),..., which is not a prefix of any other x(j), x(j + 1), for j less-than-or-equal-to n. We show that this estimator is not consistent for the general ergodic process, although it is consistent for Markov chains. A weaker trimmed mean type result is proved for the general case, namely, given epsilon > 0, eventually almost surely all but an epsilon-fract...
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作者：SOWERS, RB
摘要：In this paper we establish a large deviations principle for the non-Gaussian stochastic reaction-diffusion equation (SRDE) partial derivative(t)upsilon(epsilon) = L(upsilon)epsilon + f(x, upsilon(epsilon)) + epsilon-sigma(x, upsilon(epsilon))W(tx) as a random perturbation of the deterministic RDE partial derivative(t)upsilon-0 = L-upsilon-0 + f(x, upsilon-0). Here the space variable takes values on the unit circle S1 and L is a strongly-elliptic second-order operator with constant coefficients...
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作者：ATHREYA, KB
摘要：Let {Z(n)} be a p type positively regular nonsingular critical branching process with mean matrix M. If v is a right eigenvector of M for the eigenvalue 1 and Y(n) = Z(n) . v, and if M(n) = max0 less-than-or-equal-to j less-than-or-equal-to n Y(j), then it is shown that under second moments (log n)-1E(i)M(n) --> i . v, where E(i) denotes starting with Z0 = i and . denotes inner product. This is an extension of the result for the single type case obtained by Athreya in 1988.
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作者：KEENER, RW
摘要：Let {S(n)} be a random walk on the integers with negative drift, and let A(n) = {S(k) greater-than-or-equal-to 0, 1 less-than-or-equal-to k less-than-or-equal-to n} and A = A(infinity). Conditioning on A is troublesome because P(A) = 0 and there is no natural sigma-field of events like A. A natural definition of P(B\A) is lim(n --> infinity) P(B\A(n)). The main result here shows that this definition makes sense, at least for a large class of events B: The finite-dimensional conditional distrib...
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作者：MARCUS, MB; ROSEN, J
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Texas A&M University System; Texas A&M University College Station; Technion Israel Institute of Technology
摘要：Necessary and sufficient conditions are obtained for the almost sure joint continuity of the local time of a strongly symmetric standard Markov process X. Necessary and sufficient conditions are also obtained for the almost sure global boundedness and unboundedness of the local time and for the almost sure continuity, boundedness and unboundedness of the local time in the neighborhood of a point in the state space. The conditions are given in terms of the 1-potential density of X. The proofs r...
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作者：PEMANTLE, R
作者单位：Cornell University
摘要：The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the infection lives forever with positive probability but eventually leaves any finite set. (The survival probability is a continuous function of lambda, and the proof of this is much easier than it is for the contact process on d-dimensional integer lattices.) For...
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作者：THOMASSEN, C
摘要：The two-dimensional grid Z2 and any graph of smaller growth rate is recurrent. We show that any graph satisfying an isoperimetric inequality only slightly stronger than that of Z2 is transient. More precisely, if f(k) denotes the smallest number of vertices in the boundary of a connected subgraph with k vertices, then the graph is transient if the infinite sum SIGMA-f(k)-2 converges. This can be applied to parabolicity versus hyperbolicity of surfaces.
