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作者：Guo, Shuchen; Luo, Dejun
作者单位：Chinese Academy of Sciences
摘要：We consider moderately interacting particle systems with singular inter-action kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlin-ear Fokker-Planck equations. The approach works for the Biot-Savart and repulsive Poisson kernels.
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作者：Cerny, Jiri; Drewitz, Alexander; Schmitz, Lars
作者单位：University of Basel; University of Cologne
摘要：We investigate the uniform boundedness of the fronts of the solutions to the randomized Fisher-KPP equation and to its linearization, the parabolic Anderson model. It has been known that for the standard (i.e., deterministic) Fisher-KPP equation, as well as for the special case of a randomized Fisher-KPP equation with so-called ignition type nonlinearity, the transition front is uniformly bounded (in time). Here, we show that this property of having a uniformly bounded transition front fails t...
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作者：Isohatala, Jukka; Haskell, William B.
作者单位：National University of Singapore; Purdue University System; Purdue University
摘要：We present a new, tractable method for solving risk-aware problems over finite and infinite, discounted time-horizons where the dynamics of the con-trolled process are described using the martingale method. Supposing gen-eral Polish state and action spaces, and using the martingale characteriza-tion, we state a risk-aware dynamic optimal control problem of minimizing risk of costs described by a generic risk function. From this, we construct an alternative formulation of the optimization probl...
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作者：Leimkuhler, Benedict; Sharma, Akash; V. Tretyakov, Michael
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; University of Nottingham
摘要：A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte Carlo technique, it can be used to numerically solve linear parabolic and elliptic PDEs with Robin boundary condition. One of the key results of this paper is the use of the proposed method for computing ergodic limits, that is, expectations with respect to the...
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作者：Clement, Emmanuelle
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：In this paper, we get some convergence rates in total variation distance in approximating discretized paths of Levy driven stochastic differential equa-tions, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.
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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：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：Dirksen, Sjoerd; Mendelson, Shahar
作者单位：Utrecht University; Australian National University
摘要：We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured ma-trix (a randomly subsampled circulant matrix) and is robust to analog pre -quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed ha...
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作者：Hosseini, Bamdad; Johndrow, James E.
作者单位：University of Washington; University of Washington Seattle; University of Pennsylvania
摘要：We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spec-tral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approxima-tions of the algorithm including bounds on the closeness of Cesaro averages and other pathwise quantities via perturbation theory...
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作者：Bonnier, Patric; Liu, Chong; Oberhauser, Harald
作者单位：University of Oxford; ShanghaiTech University
摘要：Two adapted stochastic processes can have similar laws but give different results in applications such as optimal stopping, queuing theory, or stochas-tic programming. The reason is that the topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. To address such discontinuities, Aldous introduced the extended weak topology, and subsequently, Hoover and Keisler showed that both, weak topology and ...
