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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.
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作者：SANMARTIN, J
作者单位：Purdue University System; Purdue University
摘要：We consider one-dimensional stochastic differential equations of the Stratonovich type: [GRAPHICS] where Z(i) are continuous semimartingales, and A(k) are continuous finite variation processes. We extend the definition of the Fisk-Stratonovich integral for a large class of coefficients sigma(i), and under suitable conditions we prove existence and uniqueness for that equation.
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作者：BOVIER, A; PICCO, P
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider the random variables xi(beta) = SIGMA(n=0)(infinity)beta(n)epsilon(n) for beta < 1. We prove that if the epsilon(n) are i.i.d. random variables with mean zero and variance 1, then a law of the iterated logarithm holds in the sense that the cluster set of [GRAPHICS] when beta converges to one, is the interval [-1,1].
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作者：DURRETT, R; STEIF, JE
作者单位：University of Gothenburg
摘要：We consider threshold voter systems in which the threshold tau > n/2, where n is the number of neighbors, and we present results in support of the following picture of what happens starting from product measure with density 1/2. The system fixates, that is, each site flips only finitely many times. There is a critical value, theta(c), so that if tau = thetan with theta > theta(c) and n is large then most sites never flip, while for theta is-an-element-of (1/2, theta(c)) and n large, the limiti...
