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作者：Gantert, Nina; Nestoridi, Evita; Schmid, Dominik
作者单位：Technical University of Munich; Princeton University
摘要：We study mixing times of the symmetric and asymmetric simple exclu-sion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the rates in the bulk, and show that the pro-cess exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time ...
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作者：Chen, Peng; Shao, Qi-Man; Xu, Lihu
作者单位：Nanjing University of Aeronautics & Astronautics; Southern University of Science & Technology; University of Macau
摘要：We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated Ito's for-mula and Markov operator. As applications, we study the error bounds of the following three approximations: approximating a family of online stochastic gradient descents (SGDs) by a stochastic differential equation (SDE) driven by multiplicative Brownian motion, Euler-Maruyama (EM) discretization for multi-dimensional Ornstein-Uhlenbeck stable pro...
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作者：Mueller-Gronbach, Thomas; Yaroslavtseva, Larisa
作者单位：University of Passau
摘要：In the past decade, an intensive study of strong approximation of stochas-tic differential equations (SDEs) with a drift coefficient that has discontinu-ities in space has begun. In the majority of these results it is assumed that the drift coefficient satisfies piecewise regularity conditions and that the diffusion coefficient is globally Lipschitz continuous and nondegenerate at the discon-tinuities of the drift coefficient. Under this type of assumptions the best L-p-error rate obtained so ...
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作者：Chen, Louis H. Y.; Thanh, Le Van
作者单位：National University of Singapore; Vinh University
摘要：In this paper, we use Stein's method to obtain optimal bounds, both in Kolmogorov and in Wasserstein distance, in the normal approximation for the empirical distribution of the ground state of a many-interacting-worlds harmonic oscillator proposed by Hall, Deckert and Wiseman (Phys. Rev. X 4 (2014) 041013). Our bounds on the Wasserstein distance solve a conjecture of McKeague and Levin (Ann. Appl. Probab. 26 (2016) 2540-2555).
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作者：Kim, Yujin H.; Lubetzky, Eyal; Zeitouni, Ofer
作者单位：New York University; Weizmann Institute of Science
摘要：We show that in branching Brownian motion (BBM) in Rd, d > 2, the law of Rt*, the maximum distance of a particle from the origin at time t, con-verges as t -> oo to the law of a randomly shifted Gumbel random variable.
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作者：Qiu, Jinniao; Zhang, Jing
作者单位：University of Calgary; Fudan University
摘要：In this paper, we study a class of zero-sum two-player stochastic differ-ential games with the controlled stochastic differential equations and the pay-off/cost functionals of recursive type. As opposed to the pioneering work by Fleming and Souganidis [Indiana Univ. Math. J. 38 (1989) 293-314] and the seminal work by Buckdahn and Li [SIAM J. Control Optim. 47 (2008) 444- 475], the involved coefficients may be random, going beyond the Markovian framework and leading to the random upper and lowe...
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作者：Quattropani, Matteo; Sau, Federico
作者单位：Leiden University; Leiden University - Excl LUMC; University of Trieste
摘要：We analyze the L1-mixing of a generalization of the averaging process introduced by Aldous (2011). The process takes place on a growing sequence of graphs which we assume to be finite-dimensional, in the sense that the random walk on those geometries satisfies a family of Nash inequalities. As a byproduct of our analysis, we provide a complete picture of the total variation mixing of a discrete dual of the averaging process, which we call binomial splitting process. A single particle of this p...
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作者：Cuchiero, Christa; Rigger, Stefan; Svaluto-ferro, Sara
作者单位：University of Vienna; University of Verona
摘要：Supercooled Stefan problems describe the evolution of the boundary be-tween the solid and liquid phases of a substance, where the liquid is assumed to be cooled below its freezing point. Following the methodology of De-larue, Nadtochiy and Shkolnikov, we construct solutions to the one-phase one-dimensional supercooled Stefan problem through a certain McKean- Vlasov equation, which allows to define global solutions even in the presence of blow-ups. Solutions to the McKean-Vlasov equation arise ...
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作者：Rosenzweig, Matthew; Serfaty, Sylvia
作者单位：Massachusetts Institute of Technology (MIT); New York University
摘要：We consider the mean-field limit of systems of particles with singular interactions of the type -log |x| or |x|-s, with 0 < s < d - 2, and with an additive noise in dimensions d >= 3. We use a modulated-energy approach to prove a quantitative convergence rate to the solution of the corresponding limiting PDE. When s > 0, the convergence is global in time, and it is the first such result valid for both conservative and gradient flows in a singular setting on Rd. The proof relies on an adaptatio...
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作者：Yang, Jun; Rosenthal, Jeffrey S.
作者单位：University of Oxford; University of Toronto
摘要：This paper considers how to obtain MCMC quantitative convergence bounds which can be translated into tight complexity bounds in high-dimensional settings. We propose a modified drift-and-minorization ap-proach, which establishes generalized drift conditions defined in subsets of the state space. The subsets are called the large sets, and are chosen to rule out some bad states which have poor drift property when the dimension of the state space gets large. Using the large sets together with a f...
