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作者：Lejay, Antoine
作者单位：Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Inria; Universite de Lorraine
摘要：We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at 0 with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier. For this, we use a process called here the snapping out Brownian motion, whose properties are studied. As this construction is motivated by applications, for example, in brain imaging or in chemistry, a simulation scheme is also provided.
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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...
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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 ...
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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...
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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...
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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...
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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...
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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...
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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.
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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...
