The Annals of Probability

最新文章

• UNIFORM-CONVERGENCE OF MARTINGALES IN THE BRANCHING RANDOM-WALK AI翻译
  作者：BIGGINS, JD
  摘要：In a discrete-time supercritical branching random walk, let Z(n) be the point process formed by the nth generation. Let m(lambda) be the Laplace transform of the intensity measure of Z(1). Then W(n)(lambda) = integral e(-lambda-x)Z(n)(dx)/m(lambda)n, which is the Laplace transform of Z(n) normalized by its expected value, forms a martingale for any lambda with \m(lambda)\ finite but nonzero. The convergence of these martingales uniformly in lambda, for lambda lying in a suitable set, is the fi...
• LOCALIZATION AND SELECTION IN A MEAN FIELD BRANCHING RANDOM-WALK IN A RANDOM ENVIRONMENT AI翻译
  作者：FLEISCHMANN, K; GREVEN, A
  作者单位：University of Gottingen
  摘要：We consider a continuous time branching random walk on the finite set {1, 2,..., N} with totally symmetric diffusion jumps and some site-dependent i.i.d. random birth rates which are unbounded. We study this process as the time t and the space size N tend to infinity simultaneously. In the classical law of large numbers setup for spatial branching models, the growth of the population obeys an exponential limit law due to the localization of the overwhelming portion of particles in the record p...
• ON THE LARGE DEVIATION PRINCIPLE FOR STATIONARY WEAKLY DEPENDENT RANDOM-FIELDS AI翻译
  作者：BRYC, W
  摘要：The large deviation principle for the empirical field of a stationary Z(d)-indexed random field is proved under strong mixing dependence assumptions. The strong mixing coefficients considered allow us to separate the ratio-mixing condition used in the literature into a part directly responsible for the (nonuniform) large deviation principle and another one, which is used when the state space is noncompact. Results are applied to obtain variants of recent large deviation theorems for Markov cha...
• BROWNIAN EXIT DISTRIBUTIONS FROM NORMAL BALLS IN S(3)XH(3) AI翻译
  作者：HUGHES, HR
  摘要：Let X(t) be Brownian motion on a Riemannian manifold M started at m and let T be the first time X(t) exits a normal ball about m. The first exit time T for M = S3 X H-3 has the same distribution as the first exit time for M = R6. For M = S3 X H-3, T and X(T) are independent random variables.
• THE LAW OF THE ITERATED LOGARITHM FOR INDEPENDENT RANDOM-VARIABLES WITH MULTIDIMENSIONAL INDEXES AI翻译
  作者：LI, DL; RAO, MB; WANG, XC
  作者单位：Jilin University; North Dakota State University Fargo
  摘要：Let X(nBAR) nBAR is-an-element-of N(d), be a field of independent real random variables, where N(d) is the d-dimensional lattice. In this paper, the law of the iterated logarithm is established for such a field of random variables. Theorem 1 brings into focus a connection between a certain strong law of large numbers and the law of the iterated logarithm. A general technique is developed by which one can derive the strong law of large numbers and the law of the iterated logarithm, exploiting t...
• ON THE SPECTRAL SLLN AND POINTWISE ERGODIC THEOREM IN L(ALPHA) AI翻译
  作者：HOUDRE, C
  摘要：We obtain criteria for the SLLN to hold for processes which are Fourier transforms of random measures. With this spectral approach, we also give criteria for the pointwise ergodic theorem to hold, for some classes of operators between L(alpha)-spaces, 1 less-than-or-equal-to alpha < + infinity. These results apply in particular to contractions on L2. Some random fields extensions are also studied.
• AUTOMORPHISM INVARIANT-MEASURES ON TREES AI翻译
  作者：PEMANTLE, R
  作者单位：Cornell University
  摘要：Consider a collection of real-valued random variables indexed the integers. It is well known that such a process can be stationary, that is, translation invariant, and ergodic and yet have very strong associations: The one-sided tail field may determine the sample; the measure may fail to be mixing in any sense; the weak law of large numbers may fail on some infinite subset of the integers. The main result of this paper is that this cannot happen if the integers are replaced by an infinite hom...
• ON THE POSITION OF A RANDOM-WALK AT THE TIME OF 1ST EXIT FROM A SPHERE AI翻译
  作者：GRIFFIN, PS; MCCONNELL, TR
  摘要：Let T(r) be the first time a sum S(n) of nondegenerate i.i.d. random vectors leaves the sphere of radius r. The spheres are determined by some given norm on R(d) which need not be the Euclidean norm. As a particular case of our results, we obtain, for mean-zero random vectors and each 0 < p < infinity and 0 less-than-or-equal-to q < infinity, necessary and sufficient conditions on the distribution of the summands to have E(parallel-to S(T(r))parallel-to - r)P = O(r(q)) as r --> infinity. We al...
• OCCUPATION TIME LARGE DEVIATIONS FOR THE SYMMETRICAL SIMPLE EXCLUSION PROCESS AI翻译
  作者：LANDIM, C
  摘要：We obtain the decay rate of the large deviation probabilities of occupation time for the symmetric simple exclusion process. Furthermore, in dimension d not-equal 2, we prove a large deviation principle for the occupation time. To obtain these results, we prove hydrodynamical limits for the weakly asymmetric simple exclusion process and we prove a large deviation principle for the empirical density for the symmetric simple exclusion process.
• AN EXTENSION OF PITMAN THEOREM FOR SPECTRALLY POSITIVE LEVY PROCESSES AI翻译
  作者：BERTOIN, J
  摘要：If X is a spectrally positive Levy process, X(c)BAR the continuous part of its maximum process, and J the sum of the jumps of X across its previous maximum, then X - 2X(c)BAR - J has the same law as X conditioned to stay negative. This extends a result due to Pitman, who links the real Brownian motion and the three-dimensional Bessel process. Several other relations between the Brownian motion and the Bessel process are extended in this setting.