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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：Pardoux, E; Veretennikov, AY
作者单位：Aix-Marseille Universite; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：A Poisson equation in R-d for the elliptic operator corresponding to an ergodic diffusion process is considered. Existence and uniqueness of its solution in Sobolev classes of functions is established along with the bounds for its growth. This result is used to study a diffusion approximation for two-scaled diffusion processes using the method of corrector; the solution of a Poisson equation serves as a corrector.
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作者：Atar, R; Budhiraja, A; Dupuis, P
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：Let G subset of R-k be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {G(i), i = 1,..., N} where n(i) and d(i) denote the inward normal and direction of constraint associated with G(i), respectively. Stability properties of a class of diffusion processes, constrained to take values in G, are studied under the assumption that the Skorokhod problem defined by the data {(n(i), d(i)), i = 1,..., N} is well posed and the Skorokhod map is Lipschitz contin...
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作者：Fleischmann, K; Xiong, J
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Tennessee System; University of Tennessee Knoxville
摘要：In generalization of the mutually catalytic super-Brownian motion in R of Dawson and Perkins and Mytnik, a function-valued cyclically catalytic model X is constructed as a strong Markov solution to a martingale problem. Starting with a finite population X-0, each pair of neighboring types will globally segregate in the long-term limit (noncoexistence of neighboring types). Also finer extinction-survival properties depending on X-0 are studied in the spirit of Mueller and Perkins. In fact, X-0 ...
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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：Lee, TY
作者单位：University System of Maryland; University of Maryland College Park
摘要：Limit laws for three-dimensional super-Brownian motion are derived, conditioned on survival up to a large time. A large deviation principle is proved for the joint behavior of occupation times and their difference. These are done via analyzing the generating function and exploiting a connection between probability and differential-integral equations.
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作者：Levin, DA; Pemantle, R; Peres, Y
作者单位：University of Connecticut; University of Wisconsin System; University of Wisconsin Madison; Hebrew University of Jerusalem; University of California System; University of California Berkeley
摘要：Suppose that a coin with bias 9 is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let we be the distribution of the observed sequence of coin tosses, and let u(n) denote the chance of a renewal at time n. Harris and Keane showed that if Sigma(n=1)(infinity) u(n)(2)=infinity, then u(theta) and u(0) are singular, while if Sigma(n=1)(infinity) u(n)(2) < infinity and theta is small enough, then u(theta) is absolutely continuous with respect to go. They ...
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作者：Pemantle, R; Stacey, AM
作者单位：University System of Ohio; Ohio State University; University of Cambridge
摘要：We show that the branching random walk on a Galton-Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there are some Galton-Watson trees on which the branching random walk has one phase transition while the contact process has two; this contradicts a conjecture of Madras and Schinazi. We show that the contact process has only one phase transition on some trees of uniformly exponential growth and bounded deg...
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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.;...
