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作者：McSweeney, John K.; Popovic, Lea
作者单位：Rose Hulman Institute Technology; Concordia University - Canada
摘要：We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling, branching or splitting which makes unbiased perturbative changes to species amounts. Our results show that in a system with a large but bounded capacity, certain combinations of these two types of interactions can lead to stochastically-induced bistability. Dep...
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作者：Cox, J. Theodore; Perkins, Edwin A.
作者单位：Syracuse University; University of British Columbia
摘要：We prove a complete convergence theorem for a class of symmetric voter model perturbations with annihilating duals. A special case of interest covered by our results is the stochastic spatial Lotka-Volterra model introduced by Neuhauser and Pacala [Ann. Appl. Probab. 9 (1999) 1226-1259]. We also treat two additional models, the affine and geometric voter models.
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作者：Morris, Ben; Ning, Weiyang; Peres, Yuval
作者单位：University of California System; University of California Davis; University of Washington; University of Washington Seattle; Microsoft
摘要：The card-cyclic-to-random shuffle on n cards is defined as follows: at time t remove the card with label t mod n and randomly reinsert it back into the deck. Pinsky [Probabilistic and combinatorial aspects of the card-cyclic-to-random shuffle (2011). Unpublished manuscript] Introduced this shuffle and asked how many steps are needed to mix the deck. He showed n steps do not suffice. Here we show that the mixing time is on the order of Theta (n log n).
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作者：Alfonsi, A.; Jourdain, B.; Kohatsu-Higa, A.
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Ritsumeikan University; Japan Science & Technology Agency (JST)
摘要：In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Eu ler discretization with N steps is smaller than O(N-2/3+epsilon) where epsilon is an arbitrary positive constant. This rate is intermediate between the strong error estimation in O(N-1/2) obtained when coupling the stochastic differential equation and the Euler scheme with the s...
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作者：Gurvich, Itai
作者单位：Northwestern University
摘要：Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove, approximates that of the Markov chain with notable. precision. Strong approximations provide such limitless approximations for process dynamics. Our focus here is on steady-state distributions, and the diffusion model that we propose is tractable relative to ...
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作者：Spencer, Joel; Sudan, Madhu; Xu, Kuang
作者单位：New York University; Microsoft; Massachusetts Institute of Technology (MIT)
摘要：study an admissions control problem, where a queue with service rate 1 - p receives incoming jobs at rate lambda epsilon (1 - p, 1), and the decision maker is allowed to redirect away jobs up to a rate of p, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate similar to log(...
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作者：Arguin, Louis-Pierre; Zindy, Olivier
作者单位：Universite de Montreal; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
摘要：We study the statistics of the extremes of a discrete Gaussian field with logarithmic correlations at the level of the Gibbs measure. The model is defined on the periodic interval [0, 1], and its correlation structure is nonhierarchical. It is based on a model introduced by Bacry and Muzy [Comm. Math. Phys. 236 (2003) 449-475] (see also Barral and Mandelbrot [Probab. Theory Related Fields 124 (2002) 409-430]), and is similar to the logarithmic Random Energy Model studied by Carpentier and Le D...
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作者：Touboul, Jonathan
作者单位：Universite PSL; College de France
摘要：We consider the problem of the limit of bio-inspired spatially extended neuronal networks including an infinite number of neuronal types (space locations), with space-dependent propagation delays modeling neural fields. The propagation of chaos property is proved in this setting under mild assumptions on the neuronal dynamics, valid for most models used in neuroscience, in a mesoscopic limit, the neural-field limit, in which we can resolve the quite fine structure of the neuron's activity in s...
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作者：Butkovsky, Oleg
作者单位：Lomonosov Moscow State University; Technion Israel Institute of Technology
摘要：We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a good d-small set imply subgeometric convergence to the invariant measure. In the continuous time setting we obtain the same convergence rate provided that there exists a good d-small set and the Douc-Fort-Guillin supermaffingale condition holds. As an application of our results, we prove that t...
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作者：Galichon, A.; Henry-Labordere, P.; Touzi, N.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allo...
