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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...
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作者：Liao, M
作者单位：Auburn University System; Auburn University
摘要：We obtain a formula for Lyapunov exponents of stochastic flows generated by stochastic differential equations on compact manifolds. As an application, the exponents of a class of stochastic flows on spheres are determined explicitly.
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作者：Sznitman, AS
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We describe a coarse graining method, which provides lower bounds on the principal Dirichlet eigenvalue of the Laplacian in regions receiving small obstacles, and sharpens the previous method of enlargement of obstacles. Based on a quantitative Wiener criterion, one replaces the actual obstacles by obstacles of a much larger size. Controls on the shift of principal eigenvalues and capacity estimates on the locus where the Wiener criterion breaks down are derived. The results are written in a s...
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作者：Dynkin, EB; Kuznetsov, SE
作者单位：Cornell University; Russian Academy of Sciences
摘要：Suppose that E is an arbitrary domain in R-d, L is a second order elliptic differential operator in S = R+ x E and S-e is the extremal part of the Martin boundary for the corresponding diffusion xi. Let 1 < alpha less than or equal to 2. We investigate a boundary value problem partial derivative u/partial derivative r + Lu - u(alpha) = -eta inS, (*) u = v on S-e, u = 0 on {infinity} x E involving two measures eta and v. For the existence of a solution, we give sufficient conditions in terms of...
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作者：Föllmer, H; Gantert, N
作者单位：Humboldt University of Berlin; Technical University of Berlin
摘要：Schrodinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as h-transforms in the sense of Doob for some space-time harmonic function h of Brownian motion, and also as solutions to a large deviation problem introduced by Schrodinger which involves minimization of relative entropy with given marginals. As a basic case study in infinite dimensions, we investigate these different aspects for Schrodinger pro...
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作者：Bobkov, SG; Houdré, C
作者单位：Syktyvkar State University; University System of Georgia; Georgia Institute of Technology
摘要：A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived.
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作者：Chang, JT; Peres, Y
作者单位：Yale University; University of California System; University of California Berkeley; Hebrew University of Jerusalem
摘要：Let {S-n: n greater than or equal to 0} be a random walk having normally distributed increments with mean theta and variance 1, and let tau be the time at which the random walk first takes a positive value, so that S-tau is the first ladder height. Then the expected value EthetaStau, originally defined for positive theta, may be extended to be an analytic function of the complex variable theta throughout the entire complex plane, with the exception of certain branch point singularities. In par...
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作者：Rheinlander, T; Schweizer, M
作者单位：Technical University of Berlin
摘要：Let X be an R-d-valued continuous semimartingale, T a fixed time horizon and Theta the space of all R-d-valued predictable X-integrable processes such that the stochastic integral G(theta) = integral theta dX is a square-integrable semimartingale. A recent paper gives necessary and sufficient conditions on X for G(T)(Theta) to be closed in L-2(P). In this paper, we describe the structure of the L-2-projection mapping an F-T-measurable random variable H is an element of L-2(P) on GT(Theta) and ...
