2016

最新文章

• THE MEAN EULER CHARACTERISTIC AND EXCURSION PROBABILITY OF GAUSSIAN RANDOM FIELDS WITH STATIONARY INCREMENTS AI翻译
  作者：Cheng, Dan; Xiao, Yimin
  作者单位：North Carolina State University; Michigan State University
  摘要：Let X = {X (t), t is an element of R-N} be a centered Gaussian random field with stationary increments and X (0) = 0. For any compact rectangle T subset of R-N and u is an element of R, denote by A(u) = {t is an element of T : X (t) >= u} the excursion set. Under X(center dot) is an element of C-2(R-N) and certain regularity conditions, the mean Euler characteristic of A(u), denoted by E{phi(A(u))}, is derived. By applying the Rice method, it is shown that, as u -> infinity, the excursion prob...
• CONDITIONED, QUASI-STATIONARY, RESTRICTED MEASURES AND ESCAPE FROM METASTABLE STATES AI翻译
  作者：Fernandez, R.; Manzo, F.; Nardi, F. R.; Scoppola, E.; Sohier, J.
  作者单位：Utrecht University; Roma Tre University; Eindhoven University of Technology; Eindhoven University of Technology
  摘要：We study the asymptotic hitting time tau((n)) of a family of Markov processes X-(n) to a target set G((n)) when the process starts from a trap defined by very general properties. We give an explicit description of the law of X-(n) conditioned to stay within the trap, and from this we deduce the exponential distribution of tau((n).) Our approach is very broad-it does not require reversibility, the target G does not need to be a rare event and the traps and the limit on n can be of very general ...
• VISCOSITY SOLUTIONS OF FULLY NONLINEAR ELLIPTIC PATH DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS AI翻译
  作者：Ren, Zhenjie
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：This paper extends the recent work on path-dependent PDEs to elliptic equations with Dirichlet boundary conditions. We propose a notion of viscosity solution in the same spirit as [Ann. Probab. 44 (2016) 1212-1253, Part 1; Ekren, Touzi and Zhang (2016), Part 2], relying on the theory of optimal stopping under nonlinear expectation. We prove a comparison result implying the uniqueness of viscosity solution, and the existence follows from a Perron type construction using path-frozen PDEs. We als...
• RANDOM REVERSIBLE MARKOV MATRICES WITH TUNABLE EXTREMAL EIGENVALUES AI翻译
  作者：Chi, Zhiyi
  作者单位：University of Connecticut
  摘要：Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix c > 0 and p > 0. Let A(n) be the adjacency matrix of a random graph following G(n, p/n), known as the Erdos-Renyi distribution. Add c/n to each entry of A(n) and then normalize its rows. It is shown that the resulting Markov matrix has the desired properties. Its ESD weakly converges in probability to a symm...
• THE SYMPLECTIC GEOMETRY OF CLOSED EQUILATERAL RANDOM WALKS IN 3-SPACE AI翻译
  作者：Cantarella, Jason; Shonkwiler, Clayton
  作者单位：University System of Georgia; University of Georgia; Colorado State University System; Colorado State University Fort Collins
  摘要：A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. The sample space of such walks with n edges is the (2n- 3)-dimensional Riemannian manifold of equilateral closed polygons in R-3. We study closed random walks using the symplectic geometry of the (2n - 6)-dimensional quotient of the manifold of polygons by the action of the rotation group SO(3). The basic objects of st...
• EXACT FORMULAS FOR RANDOM GROWTH WITH HALF-FLAT INITIAL DATA AI翻译
  作者：Ortmann, Janosch; Quastel, Jeremy; Remenik, Daniel
  作者单位：University of Toronto; Universidad de Chile; Universidad de Chile
  摘要：We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially occupied. These complement earlier formulas of E. Lee [J. Stat. Phys. 140 (2010) 635-647] but, unlike those formulas, ours are suitable in principle for asymptotics. We also explain how our formulas are related to divergent series formulas for half-flat KPZ of Le Do...
• UNBIASEDNESS OF SOME GENERALIZED ADAPTIVE MULTILEVEL SPLITTING ALGORITHMS AI翻译
  作者：Brehier, Charles-Edouard; Gazeau, Maxime; Goudenege, Ludovic; Lelievre, Tony; Rousset, Mathias
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Toronto; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel; Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. We build an estimator of the rare event probability (and of any nonnormalized quantity associated with this event) which is unbiased, whatever the choice of the importance function and the number of replicas. This has practical consequences on the use of this algorithm, which are illustrated th...
• DENSE GRAPH LIMITS UNDER RESPONDENT-DRIVEN SAMPLING AI翻译
  作者：Athreya, Siva; Rollin, Adrian
  作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; National University of Singapore
  摘要：We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related to the invariant measure of the ergodic sequence. For specific sampling procedures, we describe the transformation explicitly.
• HACK'S LAW IN A DRAINAGE NETWORK MODEL: A BROWNIAN WEB APPROACH AI翻译
  作者：Roy, Rahul; Saha, Kumarjit; Sarkar, Anish
  作者单位：Indian Statistical Institute; Indian Statistical Institute Delhi
  摘要：Hack [Studies of longitudinal stream profiles in Virginia and Maryland (1957). Report], while studying the drainage system in the Shenandoah valley and the adjacent mountains of Virginia, observed a power law relation l similar to a(0.6) between the length l of a stream from its source to a divide and the area a of the basin that collects the precipitation contributing to the stream as tributaries. We study the tributary structure of Howard's drainage network model of headward growth and branc...
• OPTIMAL STOPPING UNDER MODEL UNCERTAINTY: RANDOMIZED STOPPING TIMES APPROACH AI翻译
  作者：Belomestny, Denis; Kraetschmer, Volker
  作者单位：University of Duisburg Essen; HSE University (National Research University Higher School of Economics)
  摘要：In this work, we consider optimal stopping problems with conditional convex risk measures of the form rho(Phi)(t)(X) = sup(Q is an element of Qt) (E-Q[-X vertical bar F-t] - E[Phi(dQ/dP)vertical bar F-t]), where Phi : [0, infinity[->[0, infinity] is a lower semicontinuous convex mapping and Q(t) stands for the set of all probability measures Q which are absolutely continuous w.r.t. a given measure P and Q = P on F-t. Here, the model uncertainty risk depends on a (random) divergence E[Phi(dQ/dP...