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作者：Beznea, L; Boboc, N
作者单位：Institute of Mathematics of the Romanian Academy; Romanian Academy; University of Bucharest
摘要：In the frame of Borel right Markov processes, we investigate, following an analytical point of view, the Revuz correspondence between classes of potential kernels and their associated measures, improving upon the results of Revuz, Azema, Getoor and Sharpe, Fitzsimmons, Fitzsimmons and Getoor and Dellacherie, Maisonneuve and Meyer. In the probabilistic approach of the problem, the kernels that occur are the potential operators of different types of homogeneous random measures. We completely cha...
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作者：Lasserre, JB; Pearce, CEM
作者单位：Centre National de la Recherche Scientifique (CNRS); University of Adelaide
摘要：We consider a Markov chain on a locally compact metric space with an absorbing set. Necessary and sufficient conditions are provided for the existence of a quasistationary probability distribution.
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作者：van den Berg, J; Kahn, J
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：It is well-known in percolation theory (and intuitively plausible) that two events of the form there is an open path from s to a are positively correlated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form there is no open path from s to t..
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作者：Dembo, A; Gandolfi, A; Kesten, H
作者单位：Stanford University; Stanford University; University of Rome Tor Vergata; Cornell University
摘要：Let {X-upsilon, upsilon epsilon Z(d)) be i.i.d. random variables, and S(xi) = Sigma (upsilon epsilon xi) X-upsilon be the weight of a lattice animal xi. Let N-n = max{S(xi) : /xi/ = n and xi contains the origin} and G(n) = max{S(xi) : xi subset of or equal to [-n, n](d)). We show that, regardless of the negative tail of the distribution of X-upsilon, if E(X-upsilon(+))(d) (log(+)(X-upsilon(+))(d+a) < +infinity or some a > 0, then first, lim(n) n(-1)N(n) = N exists, is finite and constant a.e.;...
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作者：Ma, ZM; Xiang, KN
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University; Universidade de Lisboa
摘要：We construct a continuous superprocess X on M(Rd) which is the unique weak Feller extension of the empirical process of consistent k-point motions generated by a family of differential operators. The process X differs from known Dawson-Watanabe type, Fleming-Viot type and Ornstein-Uhlenbeck type superprocesses. This new type of superprocess provides a connection between stochastic flows and measure-valued processes, and determines a stochastic coalescence which is similar to those of Smoluchow...
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作者：Krylov, NV
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The distributions of stochastic integrals are approximated by the distributions of stochastic integrals of piece-wise constant processes. The rate of approximation in some negative Sobolev spaces is estimated. Generalizations are given for problems arising in control theory.
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作者：Caputo, P; Deuschel, JD
作者单位：Technical University of Berlin
摘要：We continue our study of large deviations of the empirical measures of a massless Gaussian field on Z(d), whose covariance is given by the Green function of a long-range random walk. In this paper we extend techniques and results of Bolthausen and Deuschel to the nonlocal case of a random walk in the domain of attraction of the symmetric alpha -stable law, with alpha epsilon (0, 2 boolean AND d). In particular, we show that critical large deviations occur at the capacity scale Nd-alpha, With a...
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作者：Stef, A; Tenenbaum, G
作者单位：Universite de Lorraine
摘要：Let F, G be arbitrary distribution functions on the real line and let F, G denote their respective bilateral Laplace transforms. Let K > 0 and let h: R+ --> R+ be continuous, non-decreasing, and such that h(u) greater than or equal to Au-4 for some A > 0 and all u > 0. Under the assumptions that sup \(F) over cap (u)- (G) over cap (u)\ less than or equal to epsilon , (F) over cap (u)+ (G) over cap (u) less than or equal to h(u) (-L less than or equal to u less than or equal to L), 0 less than ...
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作者：Häggström, O
作者单位：Chalmers University of Technology
摘要：We prove uniqueness of the infinite entangled component for bond percolation on the three-dimensional cubic lattice above the entanglement critical probability. This improves earlier results by Grimmett and Holroyd.
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作者：Volkov, S
作者单位：University of Bristol
摘要：Vertex-reinforced random walk (VRRW), defined by Pemantle, is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on almost all of them, VRRW visits only finitely many vertices with a positive probability. We conjecture that on all graphs of bounded degree, this happens with probability 1, and provide a proof only for trees of this type. We distinguish between several different pa...
