The Experts below are selected from a list of 26559 Experts worldwide ranked by ideXlab platform
Diyora Salimova - One of the best experts on this subject based on the ideXlab platform.
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On stochastic differential equations with arbitrarily Slow Convergence rates for strong approximation in two space dimensions.
Proceedings. Mathematical physical and engineering sciences, 2017Co-Authors: Mate Gerencser, Arnulf Jentzen, Diyora SalimovaAbstract:In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily Slow Convergence speed and every nat...
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on stochastic differential equations with arbitrarily Slow Convergence rates for strong approximation in two space dimensions
arXiv: Numerical Analysis, 2017Co-Authors: Mate Gerencser, Arnulf Jentzen, Diyora SalimovaAbstract:In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily Slow Convergence speed and every natural number $d \in \{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of Convergence. In this paper we strengthen the above result by proving that this Slow Convergence phenomena also arises in two ($d=2$) and three ($d=3$) space dimensions.
Eugene Lavretsky - One of the best experts on this subject based on the ideXlab platform.
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analysis of Slow Convergence regions in adaptive systems
Advances in Computing and Communications, 2016Co-Authors: Oscar Nouwens, Anuradha M Annaswamy, Eugene LavretskyAbstract:We examine Convergence properties of errors in a class of adaptive systems that corresponds to adaptive control of linear time-invariant plants with state variables accessible. We demonstrate the existence of a sticking region in the error space where the state errors move with a finite velocity independent of their magnitude. We show that these properties are also exhibited by adaptive systems with closed-loop reference models which have been demonstrated to exhibit improved transient performance as well as those that include an integral control in the inner-loop. A simulation study is included to illustrate the size of this sticking region and its dependence on various system parameters.
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ACC - Analysis of Slow Convergence regions in adaptive systems
2016 American Control Conference (ACC), 2016Co-Authors: Oscar Nouwens, Anuradha M Annaswamy, Eugene LavretskyAbstract:We examine Convergence properties of errors in a class of adaptive systems that corresponds to adaptive control of linear time-invariant plants with state variables accessible. We demonstrate the existence of a sticking region in the error space where the state errors move with a finite velocity independent of their magnitude. We show that these properties are also exhibited by adaptive systems with closed-loop reference models which have been demonstrated to exhibit improved transient performance as well as those that include an integral control in the inner-loop. A simulation study is included to illustrate the size of this sticking region and its dependence on various system parameters.
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uniform asymptotic stability and Slow Convergence in adaptive systems
IFAC Proceedings Volumes, 2013Co-Authors: Benjamin Jenkins, Travis E Gibson, Anuradha M Annaswamy, Eugene LavretskyAbstract:Abstract We examine Convergence properties of errors in a class of adaptive systems that arises for scalar plants. We show that these adaptive systems are at best uniformly asymptotically stable in the large, and possess an infinite region where the trajectories move arbitrarily Slowly, i.e. stick. We show that these properties are also exhibited by adaptive systems with closed-loop reference models which have been demonstrated to exhibit improved transient performance. Despite such transient behavior, we show that the Slow Convergence can still occur and has the potential to be Slower than classic open-loop reference model adaptive systems.
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ALCOSP - Uniform Asymptotic Stability and Slow Convergence in Adaptive Systems
IFAC Proceedings Volumes, 2013Co-Authors: Benjamin Jenkins, Travis E Gibson, Anuradha M Annaswamy, Eugene LavretskyAbstract:Abstract We examine Convergence properties of errors in a class of adaptive systems that arises for scalar plants. We show that these adaptive systems are at best uniformly asymptotically stable in the large, and possess an infinite region where the trajectories move arbitrarily Slowly, i.e. stick. We show that these properties are also exhibited by adaptive systems with closed-loop reference models which have been demonstrated to exhibit improved transient performance. Despite such transient behavior, we show that the Slow Convergence can still occur and has the potential to be Slower than classic open-loop reference model adaptive systems.
Mate Gerencser - One of the best experts on this subject based on the ideXlab platform.
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On stochastic differential equations with arbitrarily Slow Convergence rates for strong approximation in two space dimensions.
Proceedings. Mathematical physical and engineering sciences, 2017Co-Authors: Mate Gerencser, Arnulf Jentzen, Diyora SalimovaAbstract:In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily Slow Convergence speed and every nat...
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on stochastic differential equations with arbitrarily Slow Convergence rates for strong approximation in two space dimensions
arXiv: Numerical Analysis, 2017Co-Authors: Mate Gerencser, Arnulf Jentzen, Diyora SalimovaAbstract:In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily Slow Convergence speed and every natural number $d \in \{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of Convergence. In this paper we strengthen the above result by proving that this Slow Convergence phenomena also arises in two ($d=2$) and three ($d=3$) space dimensions.
Arnulf Jentzen - One of the best experts on this subject based on the ideXlab platform.
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On stochastic differential equations with arbitrarily Slow Convergence rates for strong approximation in two space dimensions.
Proceedings. Mathematical physical and engineering sciences, 2017Co-Authors: Mate Gerencser, Arnulf Jentzen, Diyora SalimovaAbstract:In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily Slow Convergence speed and every nat...
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on stochastic differential equations with arbitrarily Slow Convergence rates for strong approximation in two space dimensions
arXiv: Numerical Analysis, 2017Co-Authors: Mate Gerencser, Arnulf Jentzen, Diyora SalimovaAbstract:In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily Slow Convergence speed and every natural number $d \in \{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of Convergence. In this paper we strengthen the above result by proving that this Slow Convergence phenomena also arises in two ($d=2$) and three ($d=3$) space dimensions.
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on stochastic differential equations with arbitrary Slow Convergence rates for strong approximation
arXiv: Numerical Analysis, 2015Co-Authors: Arnulf Jentzen, Thomas Mullergronbach, Larisa YaroslavtsevaAbstract:In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there exist stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that the Euler scheme converges to the solution in the strong sense but with no polynomial rate. Hairer et al.'s result naturally leads to the question whether this Slow Convergence phenomenon can be overcome by using a more sophisticated approximation method than the simple Euler scheme. In this article we answer this question to the negative. We prove that there exist SDEs with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion converges in absolute mean to the solution with a polynomial rate. Even worse, we prove that for every arbitrarily Slow Convergence speed there exist SDEs with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of Convergence.
Zhou Yong-quan - One of the best experts on this subject based on the ideXlab platform.
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Self-adaptive Step Glowworm Swarm Optimization Algorithm for Optimizing Multimodal Functions
Computer Science, 2011Co-Authors: Zhou Yong-quanAbstract:Because the GSO algorithm has Slow Convergence and low precision defects when optimizing the multi-modal function,a self-adaptive step glowworm swarm optimization(SASGSO) algorithms was proposed in this paper.This algorithm can overcome Slow Convergence and low precision defects of the GSO algorithm simultaneously it can find all peaks of the multi-modal function.Experiments show that,the SASGSO algorithm has the advantages of simple operation,easy to understand,fast Convergence rates and high precision.
