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作者：Haggstrom, O
作者单位：Chalmers University of Technology
摘要：We study dependent bond percolation on the homogeneous tree T-n of order n greater than or equal to 2 under the assumption of automorphism invariance. Excluding a trivial case, we find that the number of infinite clusters a.s. is either 0 or infinity. Furthermore, each infinite cluster a.s. has either 1, 2 or infinitely many topological ends, and infinite clusters with infinitely many topological ends have a.s. a branching,Umber greater than 1. We also show that if the marginal probability tha...
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作者：Rota, GC; Wallstrom, TC
作者单位：Massachusetts Institute of Technology (MIT); United States Department of Energy (DOE); Los Alamos National Laboratory; Catholic University of America
摘要：A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson-Charlier and Kravchuk polynomi...
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作者：Biggins, JD; Kyprianou, AE
作者单位：University of Sheffield
摘要：In the discrete-time supercritical branching random walk, there is a Kesten-Stigum type result for the martingales formed by the Laplace transform of the nth generation positions. Roughly, this says that for suitable values of the argument of the Laplace transform the martingales converge in mean provided an X log X condition holds. Here it is established that when this moment condition fails, so that the martingale converges to zero, it is possible to find a (Seneta-Heyde) renormalization of ...
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作者：Fannjiang, A; Komorowski, T
作者单位：University of California System; University of California Davis; Michigan State University
摘要：We study the asymptotic behavior of Brownian motion in steady, unbounded incompressible random flows. We prove an invariance principle for almost all realizations of random flows. The key compactness result is obtained by Moser's iterative scheme in PDE theory.
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作者：Zhang, LX
作者单位：Zhejiang University
摘要：Let (X-n; n greater than or equal to 0) be a sequence of random variables. We consider its geometrically weighted series xi(beta) = Sigma(n=0)(infinity) beta(n) X-n for 0 < beta < 1. This paper proves that xi(beta) can be approximated by Sigma(n=0)(infinity) beta(n) Y-n under some suitable conditions, where (Y-n; n greater than or equal to 0) is a sequence of independent normal random variables. Applications to the law of the iterated logarithm for xi(beta) are also discussed.
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作者：Protter, P; Talay, D
作者单位：Purdue University System; Purdue University; Inria
摘要：In relation with Monte Carlo methods to solve some integro-differential equations, we study the approximation problem of Eg(X-T) by Eg((X) over bar(T)(n)), where (X-t, 0 less than or equal to t less than or equal to T) is the solution of a stochastic differential equation governed by a Levy process (Z(t)), ((X) over bar(t)(n)) is defined by the Euler discretization scheme with step T/n. With appropriate assumptions on g(.), we show that the error Eg(X-T) - Eg((X) over bar(T)(n)) can be expande...
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作者：Krylov, NV
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Several stochastic partial differential equations are derived for multidimensional superdiffusions.
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作者：Hamana, Y
作者单位：Kyushu University
摘要：We study the fluctuation problem for the multiple point range of random walks in the two dimensional integer lattice with mean 0 and finite variance. The p-multiple point range means the number of distinct sites with multiplicity p of random walk paths before time n. The suitably normalized multiple point range is proved to converge to a constant, which is independent of the multiplicity, multiple of the renormalized self-intersection local time of a planar Brownian motion.
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作者：Klenke, A
作者单位：University of Erlangen Nuremberg
摘要：In this paper we will investigate the long time behavior of critical branching Brownian motion and (finite variance) super-Brownian motion (the so-called Dawson-Watanabe process) on R-d. These processes are known to be persistent if d greater than or equal to 3; that is, there exist nontrivial equilibrium measures. If d less than or equal to 2, they cluster; that is, the processes converge to the 0 configuration while the surviving mass piles up in so-called clusters. We study the spatial prof...
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作者：Pitman, J; Yor, M
作者单位：University of California System; University of California Berkeley
摘要：The two-parameter Poisson-Dirichlet distribution, denoted PD(alpha, theta), is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with a single parameter theta, introduced by King-man, is PD(0, theta). Known properties of PD(0, theta), including the Markov chain description due to Vershik, Shmidt and Ignatov, are generalized to the two-parameter case. The size-biased random permutation of PD(alpha, theta) is a simple resi...
