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作者：MAYERWOLF, E; ZEITOUNI, O
作者单位：Technion Israel Institute of Technology
摘要：The problem of computing the lower tail of a Gaussian norm is considered in this paper. Based on large deviations arguments, a bound on these tails is derived which is tighter than those obtained by other methods. Conditional exponential moment bounds are also derived and as an application, L2 type Onsager-Machlup functionals for diffusions are computed.
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作者：BRAMSON, M; COX, JT; GREVEN, A
作者单位：Syracuse University; University of Gottingen
摘要：We consider two critical spatial branching processes on R(d): critical branching Brownian motion, and the Dawson-Watanabe process. A basic feature of these processes is that their ergodic behavior is highly dimension-dependent. It is known that in low dimensions, d less than or equal to 2, the unique invariant measure with finite intensity is delta(0), the unit point mass on the empty state. In high dimensions, d greater than or equal to 3, there is a one-parameter family of nondegenerate inva...
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作者：BURTON, RM; GOULET, M; MEESTER, R
作者单位：Utrecht University
摘要：A stationary process {X(n)}(n epsilon Z) is said to be k-dependent if {X(n)}(n<0) is independent of {X(n)}(n>k-1). It is said to be a k-block factor of a process {Y-n} if it can be represented as X(n) = f(Y-n,...,Y-n+k-1), where f is a measurable function of k variables. Any (k + 1)-block factor of an i.i.d. process is k-dependent. We answer an old question by showing that there exists a one-dependent process which is not a k-block factor of any i.i.d. process for any k. Our method also leads ...
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作者：ZHANG, Y
摘要：Cox and Durrett proved the shape theorem of epidemics and forest fires with nearest neighbor interactions. They also conjectured that the shape theorem is still true with finite range interactions. In this paper, we answer this conjecture affirmatively. The method we develop allows us also to improve the result of Zhang and Zhang for all dimension.
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作者：ARCONES, MA; GINE, E
作者单位：University of Connecticut
摘要：Necessary and sufficient conditions for the law of large numbers and sufficient conditions for the central limit theorem for U-processes are given. These conditions are in terms of random metric entroPies. The CLT and LLN for VC subgraph classes of functions as well as for classes satisfying bracketing conditions follow as consequences of the general results. In particular, Liu's simplicial depth Process satisfies both the LLN and the CLT. Among the techniques used, randomization, decoupling i...
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作者：ADLER, RJ; ROSEN, JS
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：The Brownian and stable density processes are distribution valued processes that arise both via limiting operations on infinite collections of Brownian motions and stable Levy processes and as the solutions of certain stochastic partial differential equations. Their (self-) intersection local times (ILT's) of various orders can be defined in a manner somewhat akin to that used to define the self-intersection local times of simple R(d)-valued processes; that is, via a limiting operation involvi...
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作者：HILDEBRAND, M
作者单位：University of Michigan System; University of Michigan; Harvard University
摘要：This paper considers random processes of the form X(n+1) = a(n)X(n) + b(n) (mod p), where X0 = 0 and the sequences a(n) and b(n) are independent with a(n) identically distributed for n = 0, 1, 2.... and b(n) identically distributed for n = 0, 1, 2,... . Chung, Diaconis and Graham studied such processes where a(n) = 2 always; this paper considers more general distributions for a(n) and b(n). The question is how long does it take these processes to get close to the uniform distribution? If an is...
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作者：TUERO, A
摘要：Suppose that P and P(n), n is-an-element-of N, are probabilities on a real, separable Hilbert space, V. It is known that if P satisfies some regularity conditions and X is such that P(X) = P, then there exist mappings H(n): V --> V, such that P(Hn(X)) = P(n) and the Wasserstein distance between P(n) and P coincides with (integral\\x - H(n)(x)\\2 dp)1/2, n is-an-element-of N. In this paper we prove that the weak convergence of (P(n)) to P is enough to ensure that {H(n)(X)} converges to X in mea...
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作者：VANZANDT, T
摘要：Using a result by Landers and Rogge, it is shown that the Hausdorff metric of sigma-fields is uniformly equivalent to the metric induced by the Hausdorff distance between sets of measurable functions. An application is given to the continuity of the value of information with respect to the Hausdorff metric of sigma-fields.
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作者：LANDIM, C
摘要：We prove conservation of local equilibrium for attractive particle systems. Our method applies as well to gradient asymmetric processes with mean drift 0 under diffusive (N-2) rescaling. The hydrodynamical behavior is proved for bounded continuous initial profiles under Euler (N) rescaling and for bounded a.s. continuous profiles under diffusive rescaling. We prove that, for attractive systems, the conservation of local equilibrium follows from a law of large numbers for the density field.
