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作者：FERRARI, PA; KESTEN, H; MARTINEZ, S; PICCO, P
作者单位：Universidad de Chile; Cornell University; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider Markov processes on the positive integers for which the origin is an absorbing state. Quasi-stationary distributions (qsd's) are described as fixed points of a transformation Phi in the space of probability measures. Under the assumption that the absorption time at the origin, R, of the process starting from state x goes to infinity in probability as x --> infinity, Pie show that the existence of a qsd is equivalent to E(x)e(lambda R) < infinity for some positive lambda and x. We a...
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作者：LIGGETT, TM
摘要：The best known upper bound for the critical value lambda(c) of the basic one dimensional contact process is 2. Most techniques for finding bounds on critical values have the property that they can be modified in order to obtain improved bounds. This seemed not to be the case for the approach which yielded lambda(c) less than or equal to 2 for the basic contact process. In this paper, we propose a technique for generating better bounds in this context. To illustrate its use, we carry out the fu...
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作者：Bhatt, AG; Kallianpur, G; Karandikar, RL
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider the Zakai equation for the unnormalized conditional distribution sigma when the signal process X takes values in a complete separable metric space E and when h is a continuous, possibly unbounded function on E. It is assumed that X is a Markov process which is characterized via a martingale problem for an operator A(0). Uniqueness of solution for the measure-valued Zakai and Fujisaki-Kallianpur-Kunita equations is proved when the test functions belong to the domain of A(0). It is a...
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作者：deLara, MC
摘要：A diffusion process with smooth and nondegenerate elliptic infinitesimal generator on a manifold M induces a Riemannian metric g on M. This paper discusses in detail different symmetry properties of such a diffusion by geometric methods. Partial differential equations associated with the generator are studied likewise. With an eye to modelling and applications to filtering, relationships between symmetries of deterministic systems and symmetries of diffusion processes are delineated. The incid...
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作者：ZHENG, W
摘要：We consider conditional propagation of chaos and use it to solve a class of quasilinear equations of parabolic type. In addition, we construct a class of continuous stochastic processes associated with the above nonlinear equations. Our method imposes fewer smoothness conditions on the coefficients and allows a degenerate nonlinear weight before a divergence form operator. We hope this probabilistic approach will introduce a better microscopic picture for understanding some Stefan type problems.
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作者：WU, LM
作者单位：Wuhan University
摘要：This paper consists of three parts. In the first part, we find a common condition-the C-2-regularity-both for CLT and for moderate deviations. We show that this condition is verified in two important situations: the Lee-Yang theorem case and the FKG system case. In the second part; we apply the previous results to the additive functionals of a Markov process. By means of Feymman-Kac formula and Kato's analytic perturbation theory, we show that the Lee-Yang theorem holds under the assumption th...
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作者：Dawson, D; Li, Y; Mueller, C
作者单位：University of Rochester
摘要：We consider the one-dimensional catalytic branching process introduced by Dawson and Fleischmann, which is a modification of the super-Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On t...
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作者：BENJAMINI, I; KESTEN, H
作者单位：Cornell University
摘要：Let g be a (possibly directed) locally finite graph with countably infinite vertex set V. Let {X(upsilon): v is an element of V} be an i.i.d. family of random variables with P{X(upsilon) = 1} = 1- P{X(upsilon) = 0} = p. Finally, let xi = (xi(1),xi(2),...) be a generic element of {0,1}(N); such a xi is called a word. We say that the word xi is seen from the vertex upsilon if there exists a self-avoiding path (upsilon,upsilon(1),upsilon(2),...) on g starting at upsilon and such that X(upsilon(i)...
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作者：DURRETT, R; SCHINAZI, R
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We show that in between the two critical values for the contact process on trees, there are infinitely many extremal nontranslation invariant stationary distributions. This conclusion is reminiscent of results of Grimmett and Newman for percolation on the product of a tree with the integers where there is an intermediate phase with infinitely many infinite clusters.
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作者：Burdzy, K; SanMartin, J
作者单位：Universidad de Chile
摘要：Suppose epsilon is an element of [0, 1] and let theta(epsilon)(t) = (1 - epsilon)root 2tln(2)t. Let L(t)(epsilon) denote the amount of local time spent by Brownian motion on the curve theta(epsilon)(s) before time t. If epsilon > 0, then lim sup(t-->infinity)L(t)(epsilon)/root 2tln(2)t = 2 epsilon + o(epsilon). For epsilon = 0, a nontrivial lim sup result is obtained when the normalizing function root 2tln(2)t is replaced by g(t) = root t/ln(2)tln(3)t.
