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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：Lehec, Joseph
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Poitiers
摘要：We prove nonasymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most existing works on the topic.
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作者：Cosso, Andrea; Gozzi, Fausto; Kharroubi, Idris; Pham, Huyen; Rosestolato, Mauro
作者单位：University of Milan; Luiss Guido Carli University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; University of Salento
摘要：We study the optimal control of path-dependent McKean-Vlasov equa-tions valued in Hilbert spaces motivated by non-Markovian mean-field mod-els driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we prove the dynamic programming principle (DPP) in such a general framework. The crucial law invariance property of the value function V is rigorously obtained, which means that V can be viewed as a function on the Wasserstein space of probability measures ...
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作者：Dareiotis, Konstantinos; Gerencser, Mate; Le, Khoa
作者单位：University of Leeds; Technische Universitat Wien; Technical University of Berlin
摘要：We derive sharp strong convergence rates for the Euler-Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order alpha e (0, 1) lead to rate (1 + alpha )/2.
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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：Ligget, Thomas m.; Tang, Wenpin
作者单位：University of California System; University of California Los Angeles; Columbia University
摘要：This paper is concerned with symmetric 1-dependent colorings of the dray star graph S-d for d >= 2. We compute the critical point of the 1-dependent hard-core processes on S-d, which gives a lower bound for the number of colors needed for a 1-dependent coloring of S-d. We provide an explicit construction of a 1-dependent q-coloring for any q >= 5 of the infinite subgraph S-(1,1,infinity)(3), which is symmetric in the colors and whose restriction to any path is some symmetric 1-dependent q-colo...
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作者：Goldschmidt, Christina; Stephenson, Robin
作者单位：University of Oxford; University of Sheffield
摘要：We consider the random directed graph G(n, p) with vertex set {1, 2, ... , n} in which each of the n(n - 1) possible directed edges is present independently with probability p. We are interested in the strongly connected components of this directed graph. A phase transition for the emergence of a giant strongly connected component is known to occur at p = 1/n, with critical window p = 1/n + lambda n-4/3 for lambda e R. We show that, within this critical window, the strongly connected component...
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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：Gurvich, Itai
作者单位：Northwestern University
