The Annals of Probability

最新文章

• ON THE ALMOST SURE BEHAVIOR OF SUMS OF IID RANDOM-VARIABLES IN HILBERT-SPACE AI翻译
  作者：EINMAHL, U
  摘要：We study the almost sure behavior of sums of iid random variables satisfying the bounded LIL in Hilbert space. We show that the almost sure behavior is different from the Gaussian case, whenever the second strong moments are infinite. A law of the kappa times iterated logarithm is established which refines the bounded LIL. The interesting feature here is that contrary to the known conditions for the bounded LIL, one needs not only moment type conditions but also a nice structure of the covaria...
• MICROSCOPIC STRUCTURE OF TRAVELING WAVES IN THE ASYMMETRIC SIMPLE EXCLUSION PROCESS AI翻译
  作者：FERRARI, PA; KIPNIS, C; SAADA, E
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Universite de Rouen Normandie
  摘要：The one-dimensional nearest neighbor asymmetric simple exclusion process has been used as a microscopic approximation for the Burgers equation. This equation has travelling wave solutions. In this paper we show that those solutions have a microscopic structure. More precisely, we consider the simple exclusion process with rate p (respectively, q = 1 - p) for jumps to the right (left), 1/2 < p less-than-or-equal-to 1, and we prove the following results: There exists a measure mu on the space of...
• STRONG LIMIT-THEOREMS OF EMPIRICAL DISTRIBUTIONS FOR LARGE SEGMENTAL EXCEEDANCES OF PARTIAL-SUMS OF MARKOV VARIABLES AI翻译
  作者：DEMBO, A; KARLIN, S
  摘要：Let A1, A2,..., A(n) be generated governed by an r-state irreducible Markov chain and suppose (X(i), U(i)) are real valued independently distributed given the sequence A1, A2,..., A(n), where the joint distribution of (X(i), U(i)) depends only on the values of A(i-1) and A(i) and is of bounded support. Where A0 is started with its stationary distribution, E[X1] < 0 and the existence of a finite cycle C = {A0 = i0,..., A(k) = i(k) = i0} such that Pr{SIGMA-i(m) = 1X(i) > 0, m = 1,..., k; C} > 0 ...
• L2 RATES OF CONVERGENCE FOR ATTRACTIVE REVERSIBLE NEAREST PARTICLE-SYSTEMS - THE CRITICAL CASE AI翻译
  作者：LIGGETT, TM
  摘要：Reversible nearest particle systems are certain one-dimensional interacting particle systems whose transition rates are determined by a probability density beta(n) with finite mean on the positive integers. The reversible measure for such a system is the distribution upsilon of the stationary renewal process corresponding to this density. In an earlier paper, we proved under certain regularity conditions that the system converges exponentially rapidly in L2(upsilon) if and only if the system i...
• BOUNDARY-VALUE-PROBLEMS FOR STOCHASTIC DIFFERENTIAL-EQUATIONS AI翻译
  作者：NUALART, D; PARDOUX, E
  作者单位：Aix-Marseille Universite
  摘要：In this paper, we study stochastic differential equations with boundary conditions at the endpoints of a time interval (instead of the customary initial condition). We present existence and uniqueness results and study the Markov property of the solution. In the one-dimensional case, we prove that the solution is a Markov field iff the drift is affine.
• ON THE LINEAR PREDICTION OF MULTIVARIATE (2,P)-BOUNDED PROCESSES AI翻译
  作者：HOUDRE, C
  摘要：We develop the linear least squares prediction theory for some classes of nonstationary processes having a Fourier spectral representation. We study time domain as well as spectral domain properties for these processes, such as a Wold decomposition and a decomposition for matrix bimeasures. We also obtain an autoregressive representation for the optimum predictor.
• ON AN INDEPENDENCE CRITERION FOR MULTIPLE WIENER INTEGRALS AI翻译
  作者：KALLENBERG, O
  摘要：Ustunel and Zakai have recently obtained a necessary and sufficient condition for two multiple Wiener integrals with respect to the same Brownian motion to be independent. In the present note, the sufficiency of their condition is shown to be a simple consequence of the classical relationship between multiple Wiener integrals and Hermite polynomials. The original proofs use Malliavin calculus.
• ON THE CENTRAL-LIMIT-THEOREM FOR MARKOV-CHAINS IN RANDOM-ENVIRONMENTS AI翻译
  作者：COGBURN, R
  摘要：A functional central limit theorem is established for Markov chains in random environments under the assumption of existence of a finite invariant, ergodic measure and a mixing condition. These conditions are always satisfied when the state space is finite.
• SYMMETRY GROUPS AND TRANSLATION INVARIANT REPRESENTATIONS OF MARKOV-PROCESSES AI翻译
  作者：GLOVER, J
  摘要：The symmetry groups of the potential theory of a Markov process X(t) are used to introduce new algebraic and topological structures on the state space and the process. For example, let G be the collection of bijections phi on E which preserve the collection of excessive functions. Assume there is a transitive subgroup H of the symmetry group G such that the only map phi-epsilon-H fixing a point e epsilon-E is the identity map on E. There is a bijection PSI: E --> H so that the algebraic struct...
• HYDRODYNAMIC LIMIT OF ONE-DIMENSIONAL EXCLUSION PROCESSES WITH SPEED CHANGE AI翻译
  作者：FUNAKI, T; HANDA, K; UCHIYAMA, K
  作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
  摘要：Hydrodynamic behavior of one-dimensional homogeneous exclusion processes with speed change on periodic lattices Z/NZ, N = 1,2,3,..., is studied. For every reversible exclusion process with nearest neighbor jumps and local interactions of gradient type it is shown that under diffusion-type scaling in space and time the empirical density fields of the processes converge to a weak solution of a nonlinear diffusion equation as N goes to infinity. Two classes of examples of exclusion processes as s...