The Annals of Probability

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• An information-geometric approach to a theory of pragmatic structuring AI翻译
  作者：Ay, N
  作者单位：Max Planck Society
  摘要：Within the framework of information geometry, die interaction among units of a stochastic system is quantified in terms of the Kullback-Leibler divergence of the underlying joint probability distribution from an appropriate exponential family. In the present paper, the main example for such a family is given by the set of all factorizable random fields. Motivated by this example, the locally farthest points from an arbitrary exponential family epsilon are studied. In the corresponding dynamica...
• Time-reversal in hyperbolic s.p.d.e.'s AI翻译
  作者：Dalang, RC; Walsh, JB
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of British Columbia
  摘要：This paper studies questions of changes of variables in a class of hyperbolic stochastic partial differential equations in two variables driven by white noise. Two types of changes of variables are considered: naive changes of variables which do not involve a change of filtration, which affect the equation much as though it were deterministic, and changes of variables that do involve a change of filtration, such as time-reversals. In particular, if the process in reversed coordinates does sati...
• Spatializing random measures: Doubly indexed processes and the large deviation principle (vol 27, pg 297, 1999) AI翻译
  作者：Boucher, C; Ellis, RS; Turkington, B
  作者单位：University of Massachusetts System; University of Massachusetts Amherst
• Doob, Ignatov and optional skipping AI翻译
  作者：Simons, G; Yao, YC; Yang, LJ
  作者单位：University of North Carolina; University of North Carolina Chapel Hill; Academia Sinica - Taiwan; Michigan State University
  摘要：A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Mech. 71 (1977) 79-94], unifying and extending aspects of both.
• On stochastic differential equations driven by a Cauchy process and other stable Levy motions AI翻译
  作者：Zanzotto, PA
  作者单位：University of Udine
  摘要：We consider the class of one-dimensional stochastic differential equations d X-t = b(X-t-) dZ(t), t > 0, where b is a Beret measurable real function and Z is a strictly alpha-stable Levy process (0 < alpha < 2). Weak solutions are investigated improving previous results of the author in various ways. In particular, for the equation driven by a strictly 1-stable Levy process, a sufficient existence condition is proven. Also we extend the weak existence and uniqueness exact criteria due to Engel...
• Remarks on deviation inequalities for functions of infinitely divisible random vectors AI翻译
  作者：Houdré, C
  作者单位：University System of Georgia; Georgia Institute of Technology
  摘要：We obtain deviation inequalities for some classes of functions of infinitely divisible random vectors having finite exponential moments.
• Limit theorems for the nonattractive Domany-Kinzel model AI翻译
  作者：Katori, M; Konno, N; Tanemura, H
  作者单位：Chuo University; Yokohama National University; Chiba University
  摘要：We study the Domany-Kinzel model, which is a class of discrete time Markov processes with two parameters (p(1), p(2)) is an element of [0, 1](2) and whose states are subsets of Z, the set of integers. When p(1) = alphabeta and p(2) = alpha(2beta - beta(2)) with (alpha, beta) is an element of [0, 1](2), the process can be identified with the mixed site-bond oriented percolation model on a square lattice with the probabilities of open site alpha and of open bond beta. For the attractive case, 0 ...
• Nonlinear Kolmogorov equations in infinite dimensional spaces: The backward stochastic differential equations approach and applications to optimal control AI翻译
  作者：Fuhrman, M; Tessitore, G
  作者单位：Polytechnic University of Milan; University of Parma
  摘要：Solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations. Parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control.
• Compound Poisson process approximation AI翻译
  作者：Barbour, AD; Månsson, M
  作者单位：University of Zurich; Chalmers University of Technology
  摘要：Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.
• Laws of the iterated logarithm for the range of random walks in two and three dimensions AI翻译
  作者：Bass, RF; Kumagai, T
  作者单位：University of Connecticut; Kyoto University
  摘要：Let S-n be a random walk in Z(d) and let R-n be the range of Sn. We prove an almost sure invariance principle for R-n when d = 3 and a law of the iterated logarithm for R-n when d = 2.