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作者：OREY, S
摘要：Markov chains on a countable state space are studied under the assumption that the transition probabilities (P(n)(x,y)) constitute a stationary stochastic process. An introductory section exposing some basic results of Nawrotzki and Cogburn is followed by four sections of new results.
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作者：BERMAN, SM
摘要：Let X(t), t greater-than-or-equal-to 0, be a vector Gaussian process in R(m) whose components are i.i.d. copies of a real Gaussian process X(t) with stationary increments. Under specified conditions on the spectral distribution function used in the representation of the incremental variance function, it is shown that the self-intersection local time of multiplicity r of the vector process is jointly continuous. The dimension of the self-intersection set is estimated from above and below. The m...
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作者：BRAMSON, M; DURRETT, R; SCHONMANN, RH
作者单位：University of California System; University of California Los Angeles; Cornell University
摘要：We show that in one dimension, the contact process in a random environment has an intermediate phase in which it survives but does not grow linearly. We conjecture that this does not occur in dimensions d > 1.
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作者：KURTZ, TG; PROTTER, P
作者单位：University of Wisconsin System; University of Wisconsin Madison; Purdue University System; Purdue University
摘要：Assuming that {(X(n), Y(n))} is a sequence of cadlag processes converging in distribution to (X, Y) in the Skorohod topology, conditions are given under which the sequence {integral X(n) dY(n)} converges in distribution to integral X dY. Examples of applications are given drawn from statistics and filtering theory. In particular, assuming that (U(n), Y(n)) double-line-arrow-pointing-right (U, Y) and that F(n) --> F in an appropriate sense, conditions are given under which solutions of a sequen...
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作者：STUTE, W
摘要：We introduce a class of so-called conditional U-statistics, which generalize the Nadaraya-Watson estimate of a regression function in the same way as Hoeffding's classical U-statistic is a generalization of the sample mean. Asymptotic normality and weak and strong consistency are proved.
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作者：BARSKY, DJ; AIZENMAN, M
作者单位：New York University
摘要：For independent percolation models, it is shown that if the diagrammatic triangle condition is satisfied, then the critical exponents-delta and beta exist and take their mean-field values, generalizing the criterion introduced in 1984 by Aizenman and Newman for the mean-field value of gamma in nonoriented percolation. The results apply to a broad class of nonoriented, as well as oriented, weakly homogeneous models, in which the range of the connecting bonds need not be bounded. For the nonorie...
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作者：KINOSHITA, K; RESNICK, SI
作者单位：Cornell University
摘要：Let {X(j), 1 less-than-or-equal-to j less-than-or-equal-to n} be a sequence of iid random vectors in R(d) and S(n) = {X(j)/b(n), 1 less-than-or-equal-to j less-than-or-equal-to n}. When do there exist scaling constants b(n) --> infinity such that S(n) converges to some compact set S in R(d) almost surely (in probability)? We show that a limit set S is star-shaped (i.e., x is-an-element-of S implies tx is-an-element-of S, for 0 less-than-or-equal-to t less-than-or-equal-to 1) so that after a po...
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作者：DELTIO, PR; BLANCO, MCV
摘要：Let P = (p(ij)), i,j = 1,2,...,n be the matrix of a recurrent Markov chain with stationary vector upsilon > 0 and let R = (r(ij)), i, j = 1,2,...,n be a matrix, where r(ij) = upsilon-(i)p(ij). If R is a symmetric matrix, we improve Alpern's rotational representation of P. By this representation we characterize the reversible Markov chains.
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作者：MEERSCHAERT, MM
摘要：Regular variation is used to study the asymptotic behavior of norming operators for generalized domains of attraction. This leads to a powerful decomposition theorem. Applications include a complete, concise description of moment behavior, centering constants, convergence criteria and tail behavior for generalized domains of attraction.
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作者：LANDIM, C
摘要：We prove conservation of local equilbrium, away from the shock, for some attractive asymmetric particle systems on Z(d). The method applies to a class of particle processes which includes zero-range and simple exclusion processes. The main point in the proof is to exploit attractiveness. The hydrodynamic equation obtained is a first-order nonlinear partial differential equation which presents shock waves.
