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作者：Caputo, Pietro; Martinelli, Fabio; Sinclair, Alistair; Stauffer, Alexandre
作者单位：Roma Tre University; University of California System; University of California Berkeley
摘要：The paper concerns lattice triangulations, that is, triangulations of the integer points in a polygon in R-2 whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects in their own right and by virtue of applications in algebraic geometry. Our focus is on random triangulations in which a triangulation a has weight Ala I, where is a positive real parameter, and vertical bar sigma vertical bar is the total length of the edges in a. Empi...
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作者：Bayraktar, Erhan; Nadtochiy, Sergey
作者单位：University of Michigan System; University of Michigan
摘要：In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is obtained by weakening the assumptions of symmetry required for the classical reflection principle to work. We call this method a weak reflection principle and show that it provide...
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作者：Verzelen, Nicolas; Arias-Castro, Ery
作者单位：INRAE; University of California System; University of California San Diego
摘要：We consider the problem of detecting a tight community in a sparse random network. This is formalized as testing for the existence of a dense random subgraph in a random graph. Under the null hypothesis, the graph is a realization of an Erdos-Renyi graph on N vertices and with connection probability p(0); under the alternative, there is an unknown subgraph on n vertices where the connection probability is p(1) > p(0). In Arias-Castro and Verzelen [Ann. Statist. 42 (2014) 940- 969], we focused ...
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作者：Zhang, Hongzhong; Rodosthenous, Neofytos; Hadjiliadis, Olympia
作者单位：Columbia University; University of London; Queen Mary University London; City University of New York (CUNY) System; Hunter College (CUNY); City University of New York (CUNY) System; City University of New York (CUNY) System
摘要：We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min-max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to th...
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作者：Kazi-Tani, Nabil; Possamai, Dylan; Zhou, Chao
作者单位：Universite Claude Bernard Lyon 1; Universite PSL; Universite Paris-Dauphine; National University of Singapore
摘要：In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190]. However, on the contrary to their formulation, where they can define pathwise the density of quadratic variation of the canonical process, in our setting, the compensator of the jump measure associated to the jumps of the canonical process, which...
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作者：Iyer, Gautam; Leger, Nicholas; Pego, Robert L.
作者单位：Carnegie Mellon University
摘要：We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuous-state branching theory. In particular, this equation governs the evolution of the Levy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) almost surely. We show that a nondegenerate scaling limit of the Levy measure (and the process) exists ...
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作者：Yukich, J. E.
作者单位：Lehigh University
摘要：Let P lambda := P lambda kappa denote a Poisson point process of intensity lambda kappa on [0,1](d), d >= 2, with K a bounded density on [0,1](d) and A e (0, co). Given a closed subset M c [0, lid of Hausdorff dimension (d 1), we consider general statistics E 7,2, (x, PA, M), where the score function 4 vanishes unless the input x is close to M and where satisfies a weak spatial dependency condition. We give a rate of normal convergence for the rescaled statistics ExEPA. (X x ' lld Al/divt. as ...
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作者：Blanchet, Jose; Chen, Xinyun
作者单位：Columbia University; State University of New York (SUNY) System; Stony Brook University
摘要：This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson (possibly Markov modulated) input. In this case, we analyze the complexity of our procedure as the dimension of the network increases and show that, under certain assumptions, the algorithm has polynomial-expected termination time. Our methodology includes proc...
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作者：Bank, Peter; Kramkov, Dmitry
作者单位：Technical University of Berlin; Carnegie Mellon University
摘要：We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor's orders and trade among themselves to attain Pareto optimal allocations. We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. A...
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作者：Fuhrman, Marco; Huyen Pham
作者单位：Polytechnic University of Milan; Universite Paris Cite
摘要：We study optimal stochastic control problems for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients and gain functionals are path-dependent, and importantly we do not make any ellipticity assumptions on the SDE. We develop a control randomization approach and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with...
