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作者：Janson, Svante; Neininger, Ralph
作者单位：Goethe University Frankfurt; Uppsala University
摘要：We consider the random fragmentation process introduced by Kolmogorov, where a particle having some mass is broken into pieces and the mass is distributed among the pieces at random in such a way that the proportions of the mass shared among different daughters are specified by some given probability distribution (the dislocation law); this is repeated recursively for all pieces. More precisely, we consider a version where the fragmentation stops when the mass of a fragment is below some given...
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作者：Goldsheid, Ilya Ya.
作者单位：University of London
摘要：The main goal of this work is to study the asymptotic behaviour of hitting times of a random walk (RW) in a quenched random environment (RE) on a strip. We introduce enlarged random environments in which the traditional hitting time can be presented as a sum of independent random variables whose distribution functions form a stationary random sequence. This allows us to obtain conditions (stated in terms of properties of random environments) for a linear growth of hitting times of relevant ran...
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作者：Le, H.; Barden, D.
作者单位：University of Nottingham; University of Cambridge
摘要：We generalise, to complete, connected and locally symmetric Riemannian manifolds, the construction of coupled semimartingales X and Y given in Le and Barden (J Lond Math Soc 75: 522 - 544, 2007). When such amanifold has non-negative curvature, this makes it possible for the stochastic anti-development of the corresponding semimartingale exp(Xt) (alpha exp(Xt)(-1)(Y-t)) to be a time-changed Brownian motion with drift when X and Y are. As an application, we use the latter result to strengthen, a...
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作者：Abraham, Romain; Delmas, Jean-Francois
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Orleans
摘要：We consider the height process of a Levy process with no negative jumps, and its associated continuous tree representation. Using Levy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment...
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作者：Chen, Zhen-Qing; Fukushima, Masatoshi
作者单位：University of Washington; University of Washington Seattle; Kansai University
摘要：This paper is a continuation of the works by Fukushima-Tanaka (Ann Inst Henri Poincare Probab Stat 41: 419-459, 2005) and Chen-Fukushima-Ying (Stochastic Analysis and Application, p.153-196. The Abel Symposium, Springer, Heidelberg) on the study of one-point extendability of a pair of standard Markov processes in weak duality. In this paper, general conditions to ensure such an extension are given. In the symmetric case, characterizations of the one-point extensions are given in terms of their...
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作者：Croydon, David A.
作者单位：University of Warwick
摘要：In this article, we prove global and local (point-wise) volume and heat kernel bounds for the continuum random tree. We demonstrate that there are almost-surely logarithmic global fluctuations and log-logarithmic local fluctuations in the volume of balls of radius r about the leading order polynomial term as r similar to 0. We also show that the on-diagonal part of the heat kernel exhibits corresponding global and local fluctuations as t similar to 0 almost-surely. Finally, we prove that this ...
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作者：Watanabe, Toshiro
作者单位：University of Aizu
摘要：A serious gap in the Proof of Pakes's paper on the convolution equivalence of infinitely divisible distributions on the line is completely closed. It completes the real analytic approach to Sgibnev's theorem. Then the convolution equivalence of random sums of IID random variables is discussed. Some of the results are applied to random walks and Levy processes. In particular, results of Bertoin and Doney and of Korshunov on the distribution tail of the supremum of a random walk are improved. Fi...
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作者：Kleptsyna, M. L.; Veretennikov, A. Yu.
作者单位：University of Leeds; Le Mans Universite; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：For a class of non-uniformly ergodic Markov chains (X-n) satisfying exponential or polynomial beta-mixing, under observations (Y-n) subject to an IID noise with a positive density, it is shown that wrong initial data is forgotten in the mean total variation topology, with a certain exponential or polynomial rate.
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作者：Belinschi, Serban Teodor
作者单位：Institute of Mathematics of the Romanian Academy; Romanian Academy
摘要：We prove that the free additive convolution of two Borel probability measures supported on the real line can have a component that is singular continuous with respect to the Lebesgue measure on R only if one of the two measures is a point mass. The density of the absolutely continuous part with respect to the Lebesgue measure is shown to be analytic wherever positive and finite. The atoms of the free additive convolution of Borel probability measures on the real line have been described by Ber...
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作者：Yong, Jiongmin
作者单位：State University System of Florida; University of Central Florida
摘要：Backward stochastic Volterra integral equations (BSVIEs, for short) are studied. Notion of adapted M-solution is introduced. Well-posedness of BSVIEs is established and some regularity results are proved for the adapted M-solutions via Malliavin calculus. A Pontryagin type maximum principle is presented for optimal controls of stochastic Volterra integral equations.
