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作者：Popier, Alexandre; Zhou, Chao
作者单位：Le Mans Universite; National University of Singapore
摘要：In this work, we investigate an optimal liquidation problem under Knightian uncertainty. We obtain the value function and an optimal control characterised by the solution of a second-order BSDE with monotone generator and with a singular terminal condition.
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作者：Bally, Vlad
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Inria
摘要：We deal with f(t)(dv), the solution of the homogeneous 2D Boltzmann equation without cutoff. The initial condition f(0)(dv) may be any probability distribution (except a Dirac mass). However, for sufficiently hard potentials, the semigroup has a regularization property (see Probab. Theory Related Fields 151 (2011) 659-704): f(t)(dv) = f(t)(v) dv for every t > 0. The aim of this paper is to give upper bounds for f(t)(v), the most significant one being of type f(t)(v) <= Ct(-eta)e(-vertical bar ...
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作者：Aghajani, Reza; Ramanan, Kavita
作者单位：University of California System; University of California San Diego; Brown University
摘要：We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by N identical servers in a first-come-first-serve manner. We introduce a two-component infinite-dimensional Markov process that serves as a diffusion model for this network, in the regime where the number of servers goes to infinity and the load on the network scales as 1 - beta N-1/2 + o(N-1/2) f...
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作者：Banerjee, Sayan; Mukherjee, Debankur
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：Consider a system of N parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate A(N). When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (Math. Oper. Res. 43 (2018) 867-886) established that in the Halfin-Whitt regime where (N - lambda(N))/root N -> beta > 0 as N -> infinity, appropriately scaled occupancy...
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作者：Hwang, Jong Yun; Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Royal Institute of Technology
摘要：We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdos-Renyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a suitable condition on the sparsity, we also prove that the limiting distribution of the rescaled, shifted extremal eigenvalues is given by the GOE Tracy-Widom law with an explicit formula on the deterministic shift of the spectral edge. For the biadjacency matrix...
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作者：Li, Pei-Sen; Yang, Xu; Zhou, Xiaowen
作者单位：Renmin University of China; North Minzu University; Concordia University - Canada
摘要：In this paper, we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process: X-t = x + integral(t)(0) gamma 0(X-s)ds + integral(t)(0)integral(gamma 1(Xs-))(0) W(ds, du) +integral(t)(0)integral(infinity)(0)integral(gamma 2(Xs-))(0) z (N) over tilde (ds, dz, du) where W(dt, du) and (N) over tilde (ds, dz, du) denote a Gaussian white noise and an independent compensated spectrally positive Poisson...
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作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let x(1 ), . . . , x(n) be independent random vectors of a common p-dimensional normal distribution with population correlation matrix R-n . The sample correlation matrix (R) over cap (n) = ((r) over cap (ij))(pxp) is generated from x(1) , . . . . ,x(n) such that (r) over cap (ij) is the Pearson correlation coefficient between the ith column and the jth column of the data matrix (x(1 ), . . . , x(n))'. The matrix (R) over cap (n) is a popular object in multivariate analysis and it has many con...
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作者：Kortchemski, Igor; Richier, Loic
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We are interested in the structure of large Bienayme-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law of index alpha = 1. In stark contrast to the case alpha is an element of (1, 2], we show that a condensation phenomenon occurs: in such trees, one vertex with macroscopic degree emerges (see Figure 1). To this end, we establish limit theorems for centered downwards skip-free random walks whose steps are in the domain ...
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作者：Aghajani, Reza; Ramanan, Kavita
作者单位：University of California System; University of California San Diego; Brown University
摘要：Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent and identically distributed service times are assigned to the shortest queue among a subset of d queues chosen uniformly at random, and leave the network on completion of service. Prior work on dynamical properties of this model has focused on the case of ex...
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作者：Bank, Peter; Dolinsky, Yan
作者单位：Technical University of Berlin; Hebrew University of Jerusalem; Monash University
摘要：We study super-replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable continuous time financial market models the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies. Our second result derives nontrivial scaling limits of super-replication prices for binomial models with small fixed cos...
