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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：We derive limit theorems for. the empirical distribution function of de-volatilized increments of an Ito semimartingale observed at high frequencies. These devolatilized increments are formed by suitably rescaling and truncating the raw increments to remove the effects of stochastic volatility and large jumps. We derive the limit of the empirical c.d.f. of the adjusted increments for any Ito semimartingale whose dominant component at high frequencies has activity index of 1 < beta <= 2, where ...
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作者：Beskos, Alexandros; Crisan, Dan; Jasra, Ajay
作者单位：National University of Singapore; University of London; University College London; Imperial College London
摘要：We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on R-d for large d. It is well known [Bengtsson, Bickel and Li, In Probability and Statistics: Essays in Honor of David A. Freedman, D. Nolan and T. Speed, eds. (2008) 316-334 IMS; see also Pushing the Limits of Contemporary Statistics (2008) 318-329 IMS, Mon. Weather Rev. (2009) 136 (2009) 4629-4640] that using a single importance sampling step, one produces an a...
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作者：Foss, Sergey; Martin, James B.; Schmidt, Philipp
作者单位：Heriot Watt University; Russian Academy of Sciences; University of Oxford
摘要：We consider directed last-passage percolation on the random graph G = (V, E) where V = Z and each edge (i, j), for i < j is an element of Z, is present in E independently with some probability p is an element of (0, 1]. To every (i, j) is an element of E we attach i.i.d. random weights v(i, j) > 0. We are interested in the behaviour of w(0,n), which is the maximum weight of all directed paths from 0 to n, as n -> infinity. We see two very different types of behaviour, depending on whether E[v(...
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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...
