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作者：Boutillier, Cedric
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：In this paper, we study the bead model: beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two Consecutive beads on a wired there must be exactly one bead on each neighboring wire. We construct a one-parameter family of Gibbs measures on the bead configurations that are uniform in a certain sense. When endowed with one of these measures, this model is shown to be a determinantal point process, whose marginal on each wire...
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作者：Lindner, Alexander; Sato, Ken-iti
作者单位：Braunschweig University of Technology
摘要：Properties of the law mu of the integral f(0)(infinity) C(-N1)-dY(1), are studied, where c > 1 and {(N(1), Y(1)). t >= 0} is a bivariate Levy process such that {N(t)} and {Y(t)} are Poisson processes with parameters a and b, respectively. This is the stationary distribution of some generalized Ornstein-Uhlenbeck process. The law mu is parametrized by c, q and r, where p = 1 - q - r, q, and r are the normalized Levy measure of {(N(t), Y(t))} at the points (1, 0), (0, 1) and (1, 1) respectively....
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作者：Buckdahn, Rainer; Djehiche, Boualem; Li, Juan; Peng, Shige
作者单位：Universite de Bretagne Occidentale; Royal Institute of Technology; Shandong University; Shandong University
摘要：Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to investigate a special mean-field problem in a purely stochastic approach: for the solution (Y, Z) of a mean-field backward stochastic differential equation driven by a forward stochastic differential of McKean-Vlasov type with solution X we study a special approximati...
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作者：Damron, Michael; Sapozhnikov, Artem; Vagvoelgyi, Balint
作者单位：New York University; Vrije Universiteit Amsterdam
摘要：We study invasion percolation in two dimensions. We compare connectivity properties of the origin's invaded region to those of (a) the critical percolation cluster of the origin and (b) the incipient infinite cluster. To exhibit similarities, we show that for any k >= 1, the k-point function of the first so-called pond has the same asymptotic behavior as the probability that k points are in the critical cluster of the origin. More prominent, though, are the differences. We show that there are ...
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作者：Aurzada, Frank; Dereich, Steffen
作者单位：Technical University of Berlin
摘要：We study the small deviation problem logP(sup(t is an element of[0,1]) vertical bar X-t vertical bar <= epsilon), as epsilon -> 0, for general Levy processes X. The techniques enable us to determine the asymptotic rate for general real-valued Levy processes, which we demonstrate with many examples. As a particular consequence, we show that a Levy process with nonvanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.
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作者：Croydon, David A.
作者单位：University of Warwick
摘要：A Brownian spatial tree is defined to be a pair (T, phi), where T is the rooted real tree naturally associated with a Brownian excursion and phi is a random continuous function from T into R(d) such that, conditional on T, phi maps each arc of T to the image of a Brownian motion path in R(d) run for a time equal to the arc length. It is shown that, in high dimensions, the Hausdorff measure of arcs can be used to define an intrinsic metric d(s) on the set S := phi(T). Applications of this resul...
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作者：Nourdin, Ivan; Reveillac, Anthony
作者单位：Sorbonne Universite; Universite Paris Cite; Humboldt University of Berlin
摘要：We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.
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作者：Giacomin, Giambattista; Toninelli, Fabio Lucio
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and irrelevance that is now rigorous. In this work, we exploit interpolation and replica coupling methods to obtain sharper results on the irrelevant disorder regime of pinning models. In particular, in this regime, we compute the first order term in the expansion of the...
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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Nanterre; Sorbonne Universite
摘要：Fix nu > 0, denote by G(nu/2) a Gamma random variable with parameter nu/2 and let n >= 2 be a fixed even integer. Consider a sequence {F-k}(k >= 1) of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with valiance converging to 2 nu. As k -> infinity, we prove that F-k converges in distribution to 2G(nu/2) - nu if and only if E(F-k(4)) - 12E(F-k(3)) -> 12 nu(2) - 48 nu.
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作者：Getoor, Ronald
作者单位：University of California System; University of California San Diego
摘要：During the three decades from 1930 to 1960 J. L. Doob was, with the possible exception of Kolmogorov, the man most responsible for the transformation of the study of probability to a mathematical discipline. His accomplishments were recognized by both probabilists and other mathematicians in that he is the only person ever elected to serve as president of both the IMS and the AMS. This article is an attempt to discuss his contributions to two areas in which his work was seminal, namely, the fo...
