-
作者：Bertoin, J
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the age processes A((1)) greater than or equal to ... greater than or equal to A((n)) associated to a monotone sequence R-(1) subset of or equal to ... subset of or equal to R-(n) of regenerative sets. We obtain limit theorems in distribution for (A(t)((1)),...,A(t)((n))) and for ((1/t)A(t)((1)),..., (1/t)A(t)((n))), which correspond to multivariate versions of the renewal theorem and of the Dynkin-Lamperti theorem, respectively. Dirichlet distributions play a key role in the latter.
-
作者：Engländer, J; Pinsky, RG
作者单位：Technion Israel Institute of Technology
摘要：In this paper, we construct a measure-valued diffusion on D subset of or equal to R-d whose underlying motion is a diffusion process with absorption at the boundary corresponding to an elliptic operator L = 1/2 del . a del + b . del on D subset of or equal to R-d and whose spatially dependent branching term is of the form beta(x)z - alpha(x)z(2), x is an element of D, where beta satisfies a very general condition and alpha > 0. In the case that alpha and beta are bounded from above, we show th...
-
作者：Fang, SZ
作者单位：Universite Bourgogne Europe
摘要：The geometric stochastic analysis on the Riomannian path space developed recently gives rise to the concept of tangent processes. Roughly speaking, it is the infinitesimal version of the Girsanov theorem. Using this concept, we shall establish a formula of integration by parts on the path space over a loop group. Following the martingale method developed in Capitaine, Hsu and Ledoux, we shall prove that the logarithmic Sobolev inequality holds on the full paths. As a particular case of our res...
-
作者：Lalley, SP
作者单位：Purdue University System; Purdue University
摘要：It is known that the contact process on a homogeneous tree of degree d + 1 greater than or equal to 3 has a weak survival phase, in which the infection survives with positive probability but nevertheless eventually vacates every finite subset of the tree. It is shown in this paper that in the weak survival phase there exists a spherically symmetric invariant measure whose density decays exponentially at infinity, thus confirming a conjecture of Liggett. The proof is based on a study of the rel...
-
作者：Penrose, MD
作者单位：Durham University
摘要：Suppose X-1, X-2, X-3,... are independent random points in R-d, d greater than or equal to 2, with common density f, having connected compact support Omega with smooth boundary partial derivative Omega, with f/Omega continuous. Let M-n denote the smallest r such that the union of balls of diameter r centered at the first n points is connected. Let theta denote the volume of the unit ball. Then as n --> infinity, [GRAPHICS]
-
作者：Cerf, R; Cirillo, ENM
作者单位：Universite Paris Saclay
摘要：We consider the problem of bootstrap percolation on a three-dimensional lattice and we study its finite size Scaling behavior. Bootstrap percolation is an example of cellular automata defined on the d-dimensional lattice {1,2,..., L}(d) in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability p, occupied sites remain occupied forever, while empty sites are occupied by a particle if at least l among their 2d nearest n...
-
作者：Groeneboom, P; Jongbloed, G; Wellner, JA
作者单位：Delft University of Technology; Vrije Universiteit Amsterdam; University of Washington; University of Washington Seattle
摘要：We study the two-dimensional process of integrated Brownian motion and Brownian motion, where integrated Brownian motion is conditioned to be positive. The transition density of this process is derived from the asymptotic behavior of hitting times of the unconditioned process. Explicit expressions for the transition density in terms of confluent hypergeometric functions are derived, and it is shown how our results on the hitting time distributions imply previous results of Isozaki-Watanabe and...
-
作者：Lyons, T; Stoica, L
作者单位：Imperial College London
摘要：This paper is concerned with the integration (of 1-forms) against the Markov stochastic process associated with a second-order elliptic differential operator in divergence form. It focuses on the limiting behavior of the integral as the process leaves a fixed point or goes to infinity. This extends previous work in the area where advantage was usually taken of the fact that the operator was self adjoint and started with the associated invariant measure. Applications cue given. For example, it ...
-
作者：Seppäläinen, T
作者单位：Iowa State University
摘要：In a totally asymmetric simple K-exclusion process, particles take nearest-neighbor steps to the right on the lattice Z, under the constraint that each site contain at most K particles. We prove that such processes satisfy hydrodynamic limits under Euler scaling, and that the limit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function. Our technique requires no knowledge of the invariant measures of the process, which is essential b...
-
作者：Busnello, B
作者单位：University of Pisa
摘要：We turn the Navier-Stokes equations for a 2-dimensional viscous incompressible fluid into a system of functional integrals in the trajectory space of a suitable diffusion process. Using probabilistic techniques as Girsanov's transformation and Bismut-Elworthy formula, we prove the existence of a unique global solution of this system in a constructive way.
