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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：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：LIU, XJ
摘要：We consider infinite particle systems on a countable set S with two-particle exclusion-eating motion determined by a symmetric transition function p(x, y). This is, in a certain sense, a mixture of the exclusion process and the voter model. We discuss the dual process of this process and use the dual process to give a description of the set of invariant measures and to prove an ergodic theorem.
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作者：SZNITMAN, AS
摘要：We consider a Brownian motion in a Poissonian potential conditioned to reach a remote location. We shaw that for typical configurations the expectation of the time H to reach this goal grows at most linearly in the distance from the goal to the origin. In spite of the fact that H has no finite exponential moment, we derive three exponential estimates, one of which concerns the size of a natural lattice animal attached to the trajectory of the process up to the goal.
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作者：BENJAMINI, I; PEMANTLE, R; PERES, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda is classically estimated using the capacity of Lambda with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices and also to explain a connection found by Lyons between capacity and percolation on trees.
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作者：HOUDRE, C
摘要：Let (X(n)) be, for example, a weakly stationary sequence or a lacunary system with finite pth moment, 1 less than or equal to p less than or equal to 2, and let {a(n)} be a sequence of scalars. We obtain here conditions which ensure the almost sure convergence of the series Sigma a(n)X(n). When {X(n)} is an orthonormal sequence, the classical Rademacher-Menchov theorem is recovered. This is then applied to study the strong consistency of least squares estimates in multiple regression models.
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作者：LEURIDAN, C
摘要：Let B be a brownian motion starting at 0. We denote by L(t)(*) = max x is an element of R L(t)(*) the maximum of local times at time t. The Barlow-Yor inequalities tell us that for every p > 0, there are constants C-p > c(p) > 0 such that for every stopping time tau, c(p)E[tau(p/2)]less than or equal to E[L(tau)*(p)]less than or equal to C(p)E[tau(p/2)]. Given a fixed closed set F subset of R, we give a condition on F which is necessary and sufficient to derive similar inequalities with max(x ...
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作者：ARRATIA, R; STARK, D; TAVARE, S
摘要：Assemblies are the decomposable combinatorial constructions characterized by the exponential formula for generating functions: Sigma p(n)s(n)/n! = exp(Sigma m(i)s(i)/i!). Here p(n) is the total number of constructions that can be formed from a set of size n, and m(n) is the number of these structures consisting of a single component. Examples of assemblies include permutations, graphs, 2-regular graphs, forests of rooted or unrooted trees, set partitions and mappings of a set into itself. If a...
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作者：LEFEVRE, C; UTEV, S
作者单位：Novosibirsk State University
摘要：A so-called generalized epidemic model is considered that describes the spread of an infectious disease of the SIR type with any specified distribution for the infectious period. The statistic under study is the number of susceptibles who ultimately survive the disease. In a pioneering paper, Daniels established for a particular case that when the population is large, this variable may have a Poisson-like behavior. This result was discussed later by several authors. In the present work, a nece...
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作者：COLLET, P; MARTINEZ, S; SANMARTIN, J
作者单位：Universidad de Chile
摘要：If (X(t)) is a one-dimensional diffusion corresponding to the operator L = 1/2 partial derivative(xx) - alpha partial derivative(x) starting from x > 0 and T-a is the hitting time of a, we prove that under suitable conditions on the drift coefficient the following Limit exists: For All s > 0, For All Alpha is an element of f(s), lim(t-->infinity)P(x)(X is an element of Alpha\T-0 > t). We characterize this limit as the distribution of an h-like process, h satisfying Lh = - eta h, h(0) = 0, h'(0...
