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作者：DEMBO, A; KARLIN, S
摘要：Let A1, A2,..., A(n) be generated governed by an r-state irreducible Markov chain and suppose (X(i), U(i)) are real valued independently distributed given the sequence A1, A2,..., A(n), where the joint distribution of (X(i), U(i)) depends only on the values of A(i-1) and A(i) and is of bounded support. Where A0 is started with its stationary distribution, E[X1] < 0 and the existence of a finite cycle C = {A0 = i0,..., A(k) = i(k) = i0} such that Pr{SIGMA-i(m) = 1X(i) > 0, m = 1,..., k; C} > 0 ...
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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.
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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 ...
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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...
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作者：YAGUCHI, H
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作者：ROBERTS, GO
摘要：The problem of approximating boundary hitting times for diffusion processes, and in particular Brownian motion, is considered. Using a combination of probabilistic and function-analytic techniques, approximations for conditioned diffusion distributions are obtained. These lead to approximations for the distribution of the hitting time itself. The approximations are split into three cases depending on whether the boundary is upper case, approximation square root or lower case, and one-sided bou...
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作者：BLOUNT, D
摘要：Particles placed in N cells on the unit interval give birth or die according to linear rates. Adjacent cells are coupled by diffusion with a rate proportional to N2. Cell numbers are divided by a density parameter to represent concentrations, and the resulting space-time Markov process is compared to a corresponding deterministic model, the solution to a partial differential equation. The models are viewed as Hilbert space valued processes and compared by means of a law of large numbers and ce...
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作者：SCHURGER, K
作者单位：Australian National University
摘要：Based on two notions of almost subadditivity which were introduced by Derriennic and Schurger, two a.s. limit theorems are proved which both generalize Kingman's subadditive ergodic theorem. These results, being valid under weak moment conditions, are obtained by short proofs. One of these proofs is completely elementary and does not even make use of Birkhoff's ergodic theorem which, instead, is obtained as a by-product. Finally, an improvement of Liggett's a.s. limit theorem is given.
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作者：PEMANTLE, R
作者单位：Cornell University
摘要：Consider the nearest neighbor graph for the integer lattice Z(d) in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set of spanning graphs for Z(d). This is shown to be a tree if and only if d less-than-or-equal-to 4. In this case, the tree has only one topological end, that is, there are no doubly infinite paths. Whe...
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作者：IOFFE, D
摘要：Two algorithms for calculating rate functions for a family of measures {mu-epsilon} on a B-space X are considered. The first one is a relaxed version of the Fenchel transform type theorem for convex rate functions. The second gives conditions under which {mu-epsilon} can be replaced by a more convenient family {mu-epsilon-x} near admissible points x is-an-element-of X such that rate functions for both families coincide near x. As an example, we apply both techniques to investigate large deviat...
