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作者：Miermont, G
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
摘要：The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process (F-(t),t greater than or equal to 0) out of this tree by removing the vertices located under height t. Thanks to a self-similarity property of the stable tree, we show that the fragmentation process is also self-similar. The semigroup and other features of the fragmentation are given explicitly. Asymptotic results are given, as well as a couple of related resul...
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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) ...
