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作者：Mueller, C
作者单位：University of Rochester
摘要：We consider the equation u(tt) = Delta u + a(u)N for x is an element of R-1 or R-2. N is a Gaussian noise term, which is white noise if x is an element of R-1. If a(u) grows no faster than u(log u)(1/2-epsilon), then there is a unique solution valid for all time.
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作者：Salzano, M; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：We study the ergodic behavior of the contact process on infinite connected graphs of bounded degree. We show that the fundamental notion of complete convergence is not as well behaved as it was thought to be. In particular there are graphs for which complete convergence holds in any number of separated intervals of values of the infection parameter and fails for the other values of this parameter. We then introduce a basic invariant probability measure related to the recurrence properties of t...
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作者：Fernandez, R; Pfister, CE
作者单位：Universidade de Sao Paulo; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the question of whether the quasilocality (continuity, almost Markovianness) property of Gibbs measures remains valid under a projection on a sub-sigma-algebra. Our method is based on the construction of global specifications, whose projections yield local specifications for the projected measures. For Gibbs measures compatible with monotonicity preserving local specifications, we show that the set of configurations where quasilocality is lost is an event of the tail field. This set i...
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作者：Bolthausen, E; den Hollander, F
作者单位：University of Zurich; Radboud University Nijmegen
摘要：Consider the directed process (i, S-i)(i greater than or equal to 0) where the second component is simple random walk on Z (S-0 = 0). Define a transformed path measure by weighting each n-step path with a factor exp[lambda Sigma(1 less than or equal to i less than or equal to n) (omega(i) + h)sign(S-i)]. Here, (omega(i))(i greater than or equal to 1) is an i.i.d. sequence of random variables taking values +/- 1 with probability 1/2 lading as a random medium), while lambda is an element of [0, ...
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作者：Gnedin, AV
作者单位：University of Gottingen
摘要：A composition structure is a sequence of consistent probability distributions for compositions(ordered partitions) of n = 1, 2,.... Any composition structure can be associated with an exchangeable random composition of the set of natural numbers. Following Donnelly and Joyce, we study the problem of characterizing a generic composition structure as a convex mixture of the extreme ones. We topologize the family u of open subsets of [0, 1] so that u becomes compact and show that u is homeomorphi...
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作者：Schied, A
作者单位：Humboldt University of Berlin
摘要：This paper is concerned with the intrinsic metrics of the two main classes of superprocesses. For the Fleming-Viot process, we identify it as the Bhattacharya distance, and for Dawson-Watanabe processes, we find the Kakutani-Hellinger metric. The corresponding geometries are studied in some detail. In particular, representation formulas for geodesics and are length functionals are obtained. The relations between the two metrics yield a geometric interpretation of the identification of the Flem...
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作者：Aldous, D
作者单位：University of California System; University of California Berkeley
摘要：Let(B-t(s), 0 less than or equal to s < infinity) be reflecting inhomogeneous Brownian motion with drift t - s at time s, started with B-t(0) = 0. Consider the random graph G(n, n(-1) + tn(-4/3)), whose largest components have size of order n(2/3) Normalizing by n(-2/3), the asymptotic joint distribution of component sizes is the same as the joint distribution of excursion lengths of Bt (Corollary 2). The dynamics of merging of components as t increases are abstracted to define the multiplicat...
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作者：Shao, QM
作者单位：University of Oregon
摘要：Let {X, X-n, n greater than or equal to 1} be a sequence of independent and identically distributed random variables. The classical Cramer-Chernoff large deviation states that lim(n-->infinity) n(-1) ln P((Sigma(i=1)(n) X-i)/n greater than or equal to x) = ln rho(x) if and only if the moment generating function of X is finite in a right neighborhood of zero. This paper uses n((p-1)/p)V(n,p) = n((p-1)/p)(Sigma(i=1)(n) \X-i\(p))(1/p) (p > 1) as the normalizing constant to establish a self-normal...
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作者：Lachal, A
作者单位：Universite Claude Bernard Lyon 1
摘要：Let (B(t))(t greater than or equal to 0) be the linear Brownian motion starting at 0, and set X-n(t) = (1/n!) integral(0)(t)(t - s)(n) dB(s). Watanabe stated a law of the iterated logarithm for the process (X-1(t))(t greater than or equal to 0), among other things, This paper proposes an elementary proof of this fact, which can be extended to the general case n greater than or equal to 1. Next, we study the local asymptotic classes (upper and lower) of the (n + 1)-dimensional process U-n = (B,...
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作者：Takanobu, S
作者单位：Kanazawa University
摘要：The error estimate of the integral kernel for the Trotter product formula for Schrodinger operators is shown. A basic tool for doing so is the Feynman-Kac formula based on the pinned Brownian motion. This formula enables us to express the integral kernel in handleable form and hence estimate it. As a consequence the Trotter product formula in the L-p operator norm is obtained.
