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作者：Kharroubi, Idris; Ma, Jin; Pham, Huyen; Zhang, Jianfeng
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Southern California
摘要：We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a pro...
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作者：Najnudel, Joseph
作者单位：University of Zurich
摘要：In this article, we prove that the measures Q(T) associated to the one-dimensional Edwards' model on the interval [0. T] converge to a limit measure Q when T goes to infinity, in the following sense: for all s >= 0 and for all events A(s) depending on the canonical process only up to time s, Q(T) (A(s)) Q(A(s)). Moreover, we prove that, if P is Wiener measure, there exists a martingale (D-s)(s is an element of R+) such that Q(A(s)) = E-P(1(As) D-s), and we give an explicit expression for this ...
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作者：Kuwae, Kazuhiro
作者单位：Kumamoto University
摘要：We refine stochastic calculus for symmetric Markov processes without using time reverse operators Under some conditions on the jump functions of locally square integrable martingale additive functionals, we extend Nakao's divergence-like continuous additive functional of zero energy and the stochastic integral with respect to It under the law for quasi-everywhere starting points, which are refinements of the previous results under the law for almost everywhere starting points This refinement o...
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作者：Trapman, Pieter
作者单位：Stockholm University
摘要：We consider long-range percolation on Z(d), where the probability that two vertices at distance r are connected by an edge is given by p(r) = 1 - exp[-lambda(r)] is an element of (0, 1) and the presence or absence of different edges are independent Here, lambda(r) is a strictly positive, nonincreasing, regularly varying function We investigate the asymptotic growth of the size of the k-ball around the origin, vertical bar B(k)vertical bar, that is, the number of vertices that ale within graphd...
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作者：Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre
作者单位：Brandeis University; Universite Catholique Louvain; University of Bonn
摘要：Consider n + m nonintersecting Brownian bridges, with n of them leaving from 0 at time t = -1 and returning to 0 at time t = -1, while the m remaining ones (wanderers) go from m points a(i) to m points b(i). First, we keep m fixed and we scale a(i), b(i) appropriately with n. In the large-n limit, we obtain a new Airy process with wanderers, in the neighborhood of root 2n, the approximate location of the rightmost particle in the absence of wanderers. This new process is governed by an Airy-ty...
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作者：Peligrad, Magda; Wu, Wei Biao
作者单位：University System of Ohio; University of Cincinnati; University of Chicago
摘要：We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all regular sequences. Our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram, and it provides a nice blend of harmonic analysis, theory of stationary processes and theory of martingales.
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作者：Peccati, G.; Sole, J. L.; Taqqu, M. S.; Utzet, F.
作者单位：Universite Paris Saclay; Sorbonne Universite; Boston University; Autonomous University of Barcelona
摘要：We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Esseen bounds in Central limit theorems (CLTs) involving multiple Wiener-Ito integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Levy processes.
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作者：Tao, Terence; Vu, Van; Krishnapur, Manjunath
作者单位：University of California System; University of California Los Angeles; Rutgers University System; Rutgers University New Brunswick; Indian Institute of Science (IISC) - Bangalore
摘要：Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a...
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作者：Hsu, Elton P.; Qin, Guangnan
作者单位：Northwestern University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work is estimating the small tail probability of the crossing time between two concentric geodesic spheres by reflecting Brownian motions on the larger geodesic ball.
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作者：Pemantle, Robin; Peres, Yuval
作者单位：University of Pennsylvania; Microsoft
摘要：We consider the Ising model on a general tree under various boundary conditions: all plus, free and spin-glass. In each case, we determine when the root is influenced by the boundary values in the limit as the boundary recedes to infinity. We obtain exact capacity criteria that govern behavior at critical temperatures. For plus boundary conditions, an L-3 capacity arises. In particular, on a spherically symmetric tree that has n(alpha)b(n) vertices at level n (up to bounded factors), we prove ...
