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作者：Bencheikh, Oumaima; Jourdain, Benjamin
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：In this paper, we analyse the rate of convergence of a system of N in-teracting particles with mean-field rank-based interaction in the drift coef-ficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikov (Ann. Probab. 46 (2018) 1042-1069) to check trajectorial propagation of chaos with optimal rate N-1/2 to the associated stochastic differential equations nonlinear in the sense of McKean. We next relax the assumptions needed by Bossy (Math. Comp. 73 (2004) 7...
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作者：Junge, Matthew; Lyu, Hanbaek
作者单位：City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Ballistic annihilation is an interacting system in which particles placed throughout the real line move at preassigned velocities and annihilate upon colliding. The longstanding conjecture that in the symmetric three-velocity setting there exists a phase transition for the survival of middle-velocity particles was recently resolved by Haslegrave, Sidoravicius, and Tournier. We develop a framework based on a mass transport principle to analyze threevelocity ballistic annihilation with asymmetri...
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作者：Beffara, Vincent; Chhita, Sunil; Johansson, Kurt
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Durham University; Royal Institute of Technology
摘要：Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture...
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作者：Galeati, Lucio; Harang, Fabian A.
作者单位：University of Bonn; University of Oslo
摘要：We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the...
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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...
