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作者：Karlsson, Anders; Ledrappier, Francois
作者单位：Royal Institute of Technology; University of Notre Dame
摘要：We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds which admit a compact quotient. It also generalizes Oseledec's multiplicative ergodic theorem. In addition, we show that epsilon-shadows of any ballistic random walk with finite moment on any group eventually intersect. Some related results concerning Coxeter groups and mapping class groups are recorded...
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作者：Caballero, M. E.; Chaumont, L.
作者单位：Universidad Nacional Autonoma de Mexico; Universite Paris Cite; Sorbonne Universite
摘要：Using Lamperti's relationship between Levy processes and positive selfsimilar Markov processes (pssMp), we study the weak convergence of the law P., of a pssMp starting at x > 0, in the Skorchod space of cadlag paths, when x tends to 0. To do so, we first give conditions which allow us to construct a cadlag Markov process X-(0), starting from 0, which stays positive and verifies the scaling property. Then we establish necessary and sufficient conditions for the laws P-x to converge weakly to t...
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作者：Broman, Erik I.; Steif, Jeffrey E.
作者单位：Chalmers University of Technology
摘要：In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward epsilon-movability which will be a key tool for our analysis.
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作者：Kozakova, Iva; Meester, Ronald; Nanda, Seema
作者单位：Vrije Universiteit Amsterdam; Tata Institute of Fundamental Research (TIFR); University of Tennessee System; University of Tennessee Knoxville
摘要：We study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in R-d. The connectivity function is shown to decay superexponentially, and we identify the exact exponent. From this we also obtain the decay rate of the maximal number of points of a path through the origin. We define the generation number of a point in a component and establish its asymptotic distribution as the dimension d tends to infinity.
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作者：Lototsky, S. V.; Rozovskii, B. L.
作者单位：University of Southern California
摘要：A new method is described for constructing a generalized solution of a stochastic evolution equation. Existence, uniqueness, regularity and a probabilistic representation of this Wiener Chaos solution are established for a large class of equations. As an application of the general theory, new results are obtained for several types of the passive scalar equation.
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作者：Adamczak, Radoslaw
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler norms of the kernel matrix (i.e., norms of some multilinear operators associated with the kernel matrix). As a corollary, we derive tail inequalities for U-statistics with bounded kernels and for some multiple stochastic integrals.
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作者：Gallardo, Leonard; Yor, Marc
作者单位：Universite de Tours; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Dunkl processes are martingales as well as cadlag homogeneous Markov processes taking values in R-d and they are naturally associated with a root system. In this paper we study the jumps of these processes, we describe precisely their martingale decompositions into continuous and purely discontinuous parts and we obtain a Wiener chaos decomposition of the corresponding L-2 spaces of these processes in terms of adequate mixed multiple stochastic integrals.
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作者：Nourdin, Ivan; Simon, Thomas
作者单位：Universite de Lorraine; Universite Paris Saclay
摘要：We consider the problem of absolute continuity for the one-dimensional SDE [GRAPHICS] where Z is a real Levy process without Brownian part and a a function of class C-1 with bounded derivative. Using an elementary stratification method, we show that if the drift a is monotonous at the initial point x, then X-t is absolutely continuous for every t > 0 if and only if Z jumps infinitely often. This means that the drift term has a regularizing effect, since Z(t) itself may not have a density. We a...
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作者：Graham, B. T.; Grimmett, G. R.
作者单位：University of Cambridge
摘要：The influence theorem for product measures on the discrete space to, {0, 1}(N) may be extended to probability measures with the property of monotonicity (which is equivalent to strong positive association). Corresponding results are valid for probability measures on the cube [0, 1](N) that are absolutely continuous with respect to Lebesgue measure. These results lead to a sharp-threshold theorem for measures of random-cluster type, and this may be applied to box crossings in the two-dimensiona...
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作者：Mytnik, Leonid; Perkins, Edwin; Sturm, Anja
作者单位：Technion Israel Institute of Technology; University of British Columbia; University of Delaware
摘要：We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on R-d for d >= 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.
