The Experts below are selected from a list of 68835 Experts worldwide ranked by ideXlab platform
Quanxin Zhu - One of the best experts on this subject based on the ideXlab platform.
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Comparison Principle and stability for a class of stochastic fractional differential equations
Advances in Difference Equations, 2014Co-Authors: Zhangsong Yao, Quanxin Zhu, Yi Yao, Hongwei ZhouAbstract:In this paper, we study a class of stochastic fractional differential equations. We first establish a novel Comparison Principle for such equations. Then, we use the new Comparison Principle to obtain some stability criteria, which include the stability in probability, uniform stability in probability, asymptotic stability in probability, and p th moment exponential stability. Finally, an example is provided to illustrate the obtained results.
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Letters: Comparison Principle and stability of stochastic delayed neural networks with Markovian switching
Neurocomputing, 2014Co-Authors: Quanxin ZhuAbstract:This paper deals with the stability issue for a class of stochastic delayed neural networks with Markovian switching. The jumping parameters are determined by a continuous-time, discrete-state Markov chain. Different from the usual Lyapunov-Krasovskii functional and linear matrix inequality method, we first introduce and study a new Comparison Principle in the field of stochastic delayed neural networks. Then, we apply this new Comparison Principle to obtain several novel stability criteria of the suggested system. Moreover, an example is given to illustrate the theoretical results well.
Xia Liu - One of the best experts on this subject based on the ideXlab platform.
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New Comparison Principle and stability criteria for impulsive hybrid systems on time scales
Nonlinear Analysis: Real World Applications, 2006Co-Authors: Peiguang Wang, Xia LiuAbstract:In this paper, we develop a new Comparison Principle on time scales, and give some new stability criteria for a class of impulsive hybrid systems.
Le Chen - One of the best experts on this subject based on the ideXlab platform.
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On Comparison Principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations
Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 2017Co-Authors: Le Chen, Kunwoo KimAbstract:In this paper, we prove a sample-path Comparison Principle for the nonlinear stochastic fractional heat equation on R with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be. These results extend Mueller’s Comparison Principle on the stochastic heat equation to allow more general initial data such as the (Dirac) delta measure and measures with heavier tails than linear exponential growth at ±∞. These results generalize a recent work by Moreno Flores [25], who proves the strict positivity of the solution to the stochastic heat equation with the delta initial data. As one application, we establish the full intermittency for the equation. As an intermediate step, we prove the Holder regularity of the solution starting from measure-valued initial data, which generalizes, in some sense, a recent work by Chen and Dalang [6]. MSC 2010 subject classifications: Primary 60H15. Secondary 60G60, 35R60.
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Comparison Principle for stochastic heat equation on mathbb r d
arXiv: Probability, 2016Co-Authors: Le Chen, Jingyu HuangAbstract:We establish the strong Comparison Principle and strict positivity of solutions to the following nonlinear stochastic heat equation on $\mathbb{R}^d$ \[ \left(\frac{\partial }{\partial t} -\frac{1}{2}\Delta \right) u(t,x) = \rho(u(t,x)) \:\dot{M}(t,x), \] for measure-valued initial data, where $\dot{M}$ is a spatially homogeneous Gaussian noise that is white in time and $\rho$ is Lipschitz continuous. These results are obtained under the condition that $\int_{\mathbb{R}^d}(1+|\xi|^2)^{\alpha-1}\hat{f}(\text{d} \xi) 0$.
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On Comparison Principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations
arXiv: Probability, 2014Co-Authors: Le Chen, Kunwoo KimAbstract:In this paper, we prove a sample-path Comparison Principle for the nonlinear stochastic fractional heat equation on $\mathbb{R}$ with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be. These results extend Mueller's Comparison Principle on the stochastic heat equation to allow more general initial data such as the (Dirac) delta measure and measures with heavier tails than linear exponential growth at $\pm\infty$. These results generalize a recent work by Moreno Flores [25], who proves the strict positivity of the solution to the stochastic heat equation with the delta initial data. As one application, we establish the full intermittency for the equation. As an intermediate step, we prove the H\"older regularity of the solution starting from measure-valued initial data, which generalizes, in some sense, a recent work by Chen and Dalang [6].
Kunwoo Kim - One of the best experts on this subject based on the ideXlab platform.
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On Comparison Principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations
Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 2017Co-Authors: Le Chen, Kunwoo KimAbstract:In this paper, we prove a sample-path Comparison Principle for the nonlinear stochastic fractional heat equation on R with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be. These results extend Mueller’s Comparison Principle on the stochastic heat equation to allow more general initial data such as the (Dirac) delta measure and measures with heavier tails than linear exponential growth at ±∞. These results generalize a recent work by Moreno Flores [25], who proves the strict positivity of the solution to the stochastic heat equation with the delta initial data. As one application, we establish the full intermittency for the equation. As an intermediate step, we prove the Holder regularity of the solution starting from measure-valued initial data, which generalizes, in some sense, a recent work by Chen and Dalang [6]. MSC 2010 subject classifications: Primary 60H15. Secondary 60G60, 35R60.
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On Comparison Principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations
arXiv: Probability, 2014Co-Authors: Le Chen, Kunwoo KimAbstract:In this paper, we prove a sample-path Comparison Principle for the nonlinear stochastic fractional heat equation on $\mathbb{R}$ with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be. These results extend Mueller's Comparison Principle on the stochastic heat equation to allow more general initial data such as the (Dirac) delta measure and measures with heavier tails than linear exponential growth at $\pm\infty$. These results generalize a recent work by Moreno Flores [25], who proves the strict positivity of the solution to the stochastic heat equation with the delta initial data. As one application, we establish the full intermittency for the equation. As an intermediate step, we prove the H\"older regularity of the solution starting from measure-valued initial data, which generalizes, in some sense, a recent work by Chen and Dalang [6].
Rajan Rakkiyappan - One of the best experts on this subject based on the ideXlab platform.
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Comparison Principle for impulsive functional differential equations with infinite delays and applications
Communications in Nonlinear Science and Numerical Simulation, 2018Co-Authors: Jianhua Shen, Haydar Akça, Rajan RakkiyappanAbstract:Abstract We introduce the Razumikhin technique to Comparison Principle and establish some Comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the Comparison Principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.