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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：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：Hermon, Jonathan; Salez, Justin
作者单位：University of Cambridge; Universite Paris Cite
摘要：We show that the spectral gap of a general zero range process can be controlled in terms of the spectral gap for a single particle. This is in the spirit of Aldous' famous spectral-gap conjecture for the interchange process, now resolved by Caputo et al. Our main inequality decouples the role of the geometry (defined by the jump matrix) from that of the kinetics (specified by the exit rates). Among other consequences, the various spectral gap estimates that were so far only available on the co...
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作者：Sun, Rongfeng; Swart, Jan M.; Yu, Jinjiong
作者单位：National University of Singapore; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; New York University; NYU Shanghai
摘要：A one-dimensional interacting particle system is said to exhibit interface tightness if starting in an initial condition describing the interface between two constant configurations of different types, the process modulo translations is positive recurrent. In a biological setting, this describes two populations that do not mix, and it is believed to be a common phenomenon in one-dimensional particle systems. Interface tightness has been proved for voter models satisfying a finite second moment...
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作者：Bierkens, Joris; Roberts, Gareth O.; Zitt, Pierre-Andre
作者单位：Delft University of Technology; University of Warwick; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：The zigzag process is a piecewise deterministic Markov process which can be used in a MCMC framework to sample from a given target distribution. We prove the convergence of this process to its target under very weak assumptions, and establish a central limit theorem for empirical averages under stronger assumptions on the decay of the target measure. We use the classical Meyn-Tweedie approach (Markov Chains and Stochastic Stability (2009) Cambridge Univ. Press; Adv. in Appl. Probab. 25 (1993) ...
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作者：Damron, Michael; Gravner, Janko; Junge, Matthew; Lyu, Hanbaek; Sivakoff, David
作者单位：University System of Georgia; Georgia Institute of Technology; University of California System; University of California Davis; Duke University; University of California System; University of California Los Angeles; University System of Ohio; Ohio State University
摘要：Place a car independently with probability p at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot it parks there. Other cars can still drive over the site, but cannot park there. For a large class of transitive and unimodular graphs, we show that the root is almost surely visited infinitely many times when p >= 1/2, and only finitely many times otherwise.
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作者：Gangopadhyay, Ujan; Maulik, Krishanu
作者单位：University of Southern California; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and same is true for the drift. However, the specific application of urn models with random replacement matrices motivates us to consider stochastic approximation in a setup where both the step sizes and the drift are random, but the sequence is uniformly b...
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作者：Biagini, Francesca; Zhang, Yinglin
作者单位：University of Munich
摘要：In this paper, we introduce a sublinear conditional expectation with respect to a family of possibly nondominated probability measures on a progressively enlarged filtration. In this way, we extend the classic reduced-form setting for credit and insurance markets to the case under model uncertainty, when we consider a family of priors possibly mutually singular to each other. Furthermore, we study the superhedging approach in continuous time for payment streams under model uncertainty, and est...
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作者：Hambly, Ben; Ledger, Sean; Sojmark, Andreas
作者单位：University of Oxford; University of Bristol
摘要：We study a McKean-Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier, they cause the other particles to jump in the direction of the barrier and this feedback mechanism leads to the possibility that the system can exhibit contagious blow-ups. Using a fixed-point argument, we construct a differentiable solution up to a first explosion time. Our main contribution is a proof of uniqueness in the class of cadlag functions, which ...
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作者：Ding, Jian; Peres, Yuval; Ranade, Gireeja; Zhai, Alex
作者单位：University of Pennsylvania; Microsoft; Stanford University
摘要：We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if the system growth is large enough, then the system cannot be stabilized. This is done by showing that the probability that the state magnitude remains bounded must go to zero with time. Our proof technique recursively bounds the conditional density of the system state to bound the progress the controller can make. T...
