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作者：Uzun, HB; Alexander, KS
作者单位：University of Southern California
摘要：We consider boundary roughness for the droplet created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l(2), for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l(1/3) (log l)(-2/3). This complements the upper bound of order l(1/3) (log l)(2/3) ...
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作者：Bertoin, J; Le Gall, JF
作者单位：Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Institut Universitaire de France; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Mohle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size. We define a bridge to be a right-continuous process (B(r), r is an element of [0, 1]) with nondecreasing paths and exchangeable increments, such that B(0) = 0 and B(1) = 1. We show that flows of bridges are in one-to-one correspondence with the so-calle...
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作者：Bogdan, K; Burdzy, K; Chen, ZQ
作者单位：Wroclaw University of Science & Technology; University of Washington; University of Washington Seattle
摘要：We present several constructions of a censored stable process in an open set D subset of R, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time - we give sharp conditions for such approach in terms of the stability index alpha and the thickness of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent...
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作者：Berlinkov, A
作者单位：University of Jyvaskyla
摘要：We explore the exact packing dimension of certain random recursive constructions. In case of polynomial decay at 0 of the distribution function of random variable X, associated with the construction, we prove that it does not exist, and in case of exponential decay it is t(alpha)|log|logt||(beta), where alpha is the fractal dimension of the limit set and 1/beta is the rate of exponential decay.
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作者：Heinrich, M; Rolles, SWW
作者单位：University of Bielefeld; University of California System; University of California Los Angeles
摘要：We show that an i.i.d. uniformly colored scenery on Z observed along a random walk path with bounded jumps can still be reconstructed if there are some errors in the observations. We assume the random walk is recurrent and can reach every point with positive probability. At time k, the random walker observes the color at her present location with probability 1 - delta and an error Y-k with probability delta. The errors Y-k, k greater than or equal to 0, are assumed to be stationary and ergodic...
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作者：Li, XD
作者单位：University of Oxford
摘要：We introduce Sobolev spaces and capacities on the path space P-m0 (M) over a compact Riemannian manifold M. We prove the smoothness of the Ito map and the stochastic anti-development map in the sense of stochastic calculus of variation. We establish a Sobolev norm comparison theorem and a capacity comparison theorem between the Wiener space and the path space P-m0 (M). Moreover, we prove the tightness of (r, p)-capacities on P-m0 (M), r is an element of N, p > 1, which generalises a result due...
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作者：Kohatsu-Higa, A
作者单位：Pompeu Fabra University
摘要：In this article, we generalize the lower bound estimates for uniformly elliptic diffusion processes obtained by Kusuoka and Stroock. We define the concept of uniform elliptic random variable on Wiener space and show that with this definition one can prove a lower bound estimate of Gaussian type for its density. We apply our results to the case of the stochastic heat equation under the hypothesis of unifom ellipticity of the diffusion coefficient.
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作者：Del Moral, P; Ledoux, M; Miclo, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study Lipschitz contraction properties of general Markov kernels seen as operators on spaces of probability measures equipped with entropy-like distances''. Universal quantitative bounds on the associated ergodic constants are deduced from Dobrushin's ergodic coefficient. Strong contraction properties in Orlicz spaces for relative densities are proved under more restrictive mixing assumptions. We also describe contraction bounds in the entropy sense around arbitrary probability measures by ...
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作者：Virág, B
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Ito's excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint. The index is computed and equals 1/2.
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作者：Borovkov, AA
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：Let X-1, X-2, . . . be independent identically distributed random variables with regularly varying distribution tails: P(X-1 > t) = V(t) equivalent to t(-beta) L (t), P(X-1 < -t) = W(t) equivalent to t(-alpha) L-W(t), where alpha less than or equal to min(1, beta), and L and L-W are slowly varying functions as t --> infinity. Set S-n = X-1 + (. . .) + X-n, (S) over bar (n) = max(0less than or equal tokless than or equal ton) S-k. We find the asymptotic behavior of P(S-n > x) --> 0 and P(S (S) ...
