The Annals of Probability

最新文章

• Superprocesses of stochastic flows AI翻译
  作者：Ma, ZM; Xiang, KN
  作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University; Universidade de Lisboa
  摘要：We construct a continuous superprocess X on M(Rd) which is the unique weak Feller extension of the empirical process of consistent k-point motions generated by a family of differential operators. The process X differs from known Dawson-Watanabe type, Fleming-Viot type and Ornstein-Uhlenbeck type superprocesses. This new type of superprocess provides a connection between stochastic flows and measure-valued processes, and determines a stochastic coalescence which is similar to those of Smoluchow...
• Brownian-time processes: The PDE connection and the half-derivative generator AI翻译
  作者：Allouba, H; Zheng, W
  作者单位：Indiana University System; Indiana University Bloomington; East China Normal University; University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst
  摘要：We introduce a class of interesting stochastic processes based on Brownian-time processes. These are obtained by taking Markov processes and replacing the time parameter with the modulus of Brownian motion. They generalize the iterated Brownian motion (IBM) of Burdzy and the Markov snake of Le Gall, and they introduce new interesting examples. After defining Brownian-time processes, we relate them to fourth order parabolic partial differential equations (PDE's). We then study their exit proble...
• Continuum limit for some growth models II AI翻译
  作者：Rezakhanlou, F
  作者单位：University of California System; University of California Berkeley
  摘要：We continue our investigations on a class of growth models introduced in a previous paper. Given a nonnegative function upsilon: Z(d) --> Z with upsilon(0) = 0, we define the space of configurations F to consist of functions h: Zd Z such that h(i)-h(j) < upsilon(i-j) for all i, j is an element of Z(d). We then take two sequences of independent Poisson clocks (p(+/-) (i, t): i is an element of Z(d)) of rates lambda(+/-). We start with a possibly random configuration h is an element of Gamma. Th...
• Large deviations for a Brownian motion in a drifted Brownian potential AI翻译
  作者：Taleb, M
  作者单位：Universite Paris Cite
  摘要：We derive a large deviation principle both quenched and annealed for a one-dimensional diffusion process in a drifted Brownian environment providing the continuous time analogue of what Comets, Gantert and Zeitouni recently establish for the random walk in random environment. A key-ingredient, Kotani's lemma, allows us to compute the corresponding rate functions. The results are more explicit than in the discrete-time setting.
• Geodesics and spanning trees for euclidean first-passage percolation AI翻译
  作者：Howard, CD; Newman, CM
  作者单位：City University of New York (CUNY) System; Baruch College (CUNY); New York University
  摘要：The metric D-alpha(q, q ') on the set Q of particle locations of a homogeneous Poisson process on R-d, defined as the infimum of (Sigmai \q(i) - q(i+1)\ (alpha))(1/alpha) over sequences in Q starting with q and ending with q ' (where \ (.)\ denotes Euclidean distance) has nontrivial geodesics when alpha > 1. The cases 1 < alpha < infinity are the Euclidean first-passage percolation (FPP) models introduced earlier by the authors, while the geodesics in the case alpha = infinity are exactly the ...
• Isoperimetry for Gibbs measures AI翻译
  作者：Zegarlinski, B
  作者单位：Imperial College London
  摘要：We show that a strong mixing condition implies a Bakry-Bobkov-Ledoux inequality for a probability measure on infinite-dimensional space.
• Stochastic two dimensional Euler equations AI翻译
  作者：Brzezniak, Z; Peszat, S
  作者单位：University of Hull; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
  摘要：The existence of a martingale solution to 2-dimensional stochastic Euler equations is proved. The constructed solution is a limit as the viscosity converges to zero of a sequence of solutions to modified Navier-Stokes equations.
• Stable processes on the boundary of a regular tree AI翻译
  作者：Marchal, P
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We define a class of processes on the boundary of a regular tree that can be viewed as stable Levy processes on (Z/n(0)Z)(N). We show that the range of these processes can be compared with a Bernoulli percolation as in Peres which easily leads to various results on the intersection properties. We develop an alternative approach based on the comparison with a branching random walk. By this method we establish the existence of points of infinite multiplicity when the index of the process equals ...
• A classification of coalescent processes for haploid exchangeable population models AI翻译
  作者：Möhle, M; Sagitov, S
  作者单位：Johannes Gutenberg University of Mainz; Chalmers University of Technology; University of Gothenburg
  摘要：We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as N --> infinity. It results in a full classification of the coalescent generators in the case of exchangeable reproduction. In general the coalescent process allows for simultaneous multiple mergers of ancestral lines.
• Dominos and the Gaussian free field AI翻译
  作者：Kenyon, R
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
  摘要：We define a scaling limit of the height function on the domino tiling model (dimer model) on simply connected regions in Z(2) and show that it is the massless free field, a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.