2001

最新文章

• Invariance principles with logarithmic averaging for Markov processes AI翻译
  作者：Maaoula, F
  作者单位：Universite de Tunis-El-Manar; Faculte des Sciences de Tunis (FST)
  摘要：We extend the almost-sure central limit theorem to martingale additive functionals of a recurrent Markov process. In the particular case of positive recurrence, we also derive two invariance principles similar to the central limit theorem and the law of the iterated logarithm.
• Markov chains indexed by -N: Existence and behaviour AI翻译
  作者：Brossard, J; Leuridan, C
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• Power-law corrections to exponential decay of connectivities and correlations in lattice models AI翻译
  作者：Alexander, KS
  作者单位：University of Southern California
  摘要：Consider a translation-invariant bond percolation model on the integer lattice which has exponential decay of connectivities, that is, the probability of a connection 0 <----> x by a path of open bonds decreases like exp(-m(theta)\x \) for some positive constant m(theta) which may depend on the direction a = x/\x \. In two and three dimensions, it is shown that if the model has an appropriate mixing property and satisfies a special case of the FKG property, then there is at most a power-law co...
• Strongly supermedian kernels and Revuz measures AI翻译
  作者：Beznea, L; Boboc, N
  作者单位：Institute of Mathematics of the Romanian Academy; Romanian Academy; University of Bucharest
  摘要：In the frame of Borel right Markov processes, we investigate, following an analytical point of view, the Revuz correspondence between classes of potential kernels and their associated measures, improving upon the results of Revuz, Azema, Getoor and Sharpe, Fitzsimmons, Fitzsimmons and Getoor and Dellacherie, Maisonneuve and Meyer. In the probabilistic approach of the problem, the kernels that occur are the potential operators of different types of homogeneous random measures. We completely cha...
• On the Poisson equation and diffusion approximation. I AI翻译
  作者：Pardoux, E; Veretennikov, AY
  作者单位：Aix-Marseille Universite; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
  摘要：A Poisson equation in R-d for the elliptic operator corresponding to an ergodic diffusion process is considered. Existence and uniqueness of its solution in Sobolev classes of functions is established along with the bounds for its growth. This result is used to study a diffusion approximation for two-scaled diffusion processes using the method of corrector; the solution of a Poisson equation serves as a corrector.
• On positive recurrence of constrained diffusion processes AI翻译
  作者：Atar, R; Budhiraja, A; Dupuis, P
  作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University
  摘要：Let G subset of R-k be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {G(i), i = 1,..., N} where n(i) and d(i) denote the inward normal and direction of constraint associated with G(i), respectively. Stability properties of a class of diffusion processes, constrained to take values in G, are studied under the assumption that the Skorokhod problem defined by the data {(n(i), d(i)), i = 1,..., N} is well posed and the Skorokhod map is Lipschitz contin...
• A cyclically catalytic super-Brownian motion AI翻译
  作者：Fleischmann, K; Xiong, J
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Tennessee System; University of Tennessee Knoxville
  摘要：In generalization of the mutually catalytic super-Brownian motion in R of Dawson and Perkins and Mytnik, a function-valued cyclically catalytic model X is constructed as a strong Markov solution to a martingale problem. Starting with a finite population X-0, each pair of neighboring types will globally segregate in the long-term limit (noncoexistence of neighboring types). Also finer extinction-survival properties depending on X-0 are studied in the spirit of Mueller and Perkins. In fact, X-0 ...
• On the existence of a quasistationary measure for a Markov chain AI翻译
  作者：Lasserre, JB; Pearce, CEM
  作者单位：Centre National de la Recherche Scientifique (CNRS); University of Adelaide
  摘要：We consider a Markov chain on a locally compact metric space with an absorbing set. Necessary and sufficient conditions are provided for the existence of a quasistationary probability distribution.
• A correlation inequality for connection events in percolation AI翻译
  作者：van den Berg, J; Kahn, J
  作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
  摘要：It is well-known in percolation theory (and intuitively plausible) that two events of the form there is an open path from s to a are positively correlated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form there is no open path from s to t..
• Asymptotic results for super-Brownian motions and semilinear differential equations AI翻译
  作者：Lee, TY
  作者单位：University System of Maryland; University of Maryland College Park
  摘要：Limit laws for three-dimensional super-Brownian motion are derived, conditioned on survival up to a large time. A large deviation principle is proved for the joint behavior of occupation times and their difference. These are done via analyzing the generating function and exploiting a connection between probability and differential-integral equations.