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作者：Monoyios, Michael
作者单位：University of Oxford
摘要：We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local) martingale deflators, we use a class of supermartingale deflators such that deflated wealth plus cumulative deflated consumption is a supermartingale for all admissible consumption plans. This yields a strong duality, because the enlarged dual domain of processes d...
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作者：Chen, Yu-Ting
作者单位：University of Victoria
摘要：We study some SDEs derived from the q -> 1 limit of a 2D surface growth model called the q-Whittaker process. The fluctuations are proven to exhibit Gaussian characteristics that come down from infinity: After rescaling and re-centering, convergences to the time-inverted stationary additive stochastic heat equation (SHE) hold. The point of view in this paper is a novel probabilistic representation of the SDEs by independent sums. By this connection, the normal and Poisson approximations, both ...
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作者：Ernst, Philip A.; Peskir, Goran
作者单位：Rice University; University of Manchester
摘要：Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a (known) nonzero drift permanently. Given that the position of the Brownian particle is being observed in real time, the problem is to detect the time at which a coordinate process gets the drift as accurately as possible. We solve this problem in the most uncert...
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作者：Hager, Paul; Neuman, Eyal
作者单位：Humboldt University of Berlin; Imperial College London
摘要：We consider a family of fractional Brownian fields {B-H} H is an element of(0,1) on R-d, where H denotes their Hurst parameter. We first define a rich class of normalizing kernels psi and we rescale the normalised field by the square-root of the gamma function Gamma(H), such that the covariance of X-H (x) = Gamma(H)(1/2) (B-H(x)- integral(Rd) B-H (u)Psi(u, x) du), converges to the covariance of a log-correlated Gaussian field when H down arrow 0. We then use Berestycki's good points approach (...
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作者：Han, Qiyang; Kato, Kengo
作者单位：Rutgers University System; Rutgers University New Brunswick; Cornell University
摘要：A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the distributional limit in many nonregular statistical estimation problems, the accuracy of Chernoff-type approximations has remained largely unknown. In the present paper, we tackle this problem and derive Berry-Esseen bounds for Chernoff-type limit distributions i...
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作者：Borst, Sem; den Hollander, Frank; Nardi, Francesca Romana; Taati, Siamak
作者单位：Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University; University of Florence; University of Groningen
摘要：In this paper, we study the performance of a bipartite network in which customers arrive at the nodes of the network, but not all nodes are able to serve their customers at all times. Each node can be either active or inactive, and two nodes connected by a bond cannot be active simultaneously. This situation arises in wireless random-access networks where, due to destruc-tive interference, stations that are close to each other cannot use the same frequency band. We consider a model where the n...
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作者：Bufetov, Alexey; Ferrari, Patrik L.
作者单位：University of Bonn
摘要：We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the...
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作者：Blanca, Antonio; Caputo, Pietro; Parisi, Daniel; Sinclair, Alistair; Vigoda, Eric
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Roma Tre University; University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
摘要：We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice Z(d). This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is nonlocal, that is, it changes the entire configuration in one step. We prove that, whenever strong spatial mixing (SSM) holds, the mixing time on any n-vertex cube in Z(d) is O (log n), and we prove this is tight by establishing a matching lower bound on the mixing time...
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作者：Kramkov, Dmitry; Xu, Yan
作者单位：Carnegie Mellon University
摘要：We study a single-period optimal transport problem on R-2 with a covariance-type cost function c(x,y)=(x(1)-y(1))(x(2)-y(2)) and a backward martingale constraint. We show that a transport plan gamma is optimal if and only if there is a maximal monotone set G that supports the x-marginal of gamma and such that c(x, y) = min(z is an element of G) c(z,y) for every (x,y) is an element of supp gamma. We obtain sharp regularity conditions for the uniqueness of an optimal plan and for its representat...
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作者：Lacoin, Hubert
摘要：In the present paper, we show that (under some minor technical assumption) Complex Gaussian multiplicative chaos defined as the complex exponential of a log-correlated Gaussian field can be obtained by taking the limit of the exponential of the field convoluted with a smoothing kernel. We consider two types of chaos: e(gamma)(X) for a log correlated field X and gamma = alpha + i beta, alpha, beta is an element of R and e(alpha X+)(i beta)(Y) for X and Y two independent fields with alpha, beta ...
