Although excluded from the standard account of the history of philosophy, Catharine Trotter Cockbum （1679-1749）avoided the 17th-century bias against female intellectual skills and was an active contributor to the ea...Although excluded from the standard account of the history of philosophy, Catharine Trotter Cockbum （1679-1749）avoided the 17th-century bias against female intellectual skills and was an active contributor to the early modemphilosophical discourse. In her Defence of Mr Locke＇s Essay （1702）, she defended Locke from several criticisms byThomas Burnet （1635-1715）. By analysing three of Bumet＇s main arguments, such as the theory of naturalconscience, his anti-voluntarism, and his belief in the immateriality of the soul, Trotter showed that he oftenmisinterpreted John Locke＇s principles, especially those concerning his moral epistemology.展开更多
This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in...This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
文摘Although excluded from the standard account of the history of philosophy, Catharine Trotter Cockbum （1679-1749）avoided the 17th-century bias against female intellectual skills and was an active contributor to the early modemphilosophical discourse. In her Defence of Mr Locke＇s Essay （1702）, she defended Locke from several criticisms byThomas Burnet （1635-1715）. By analysing three of Bumet＇s main arguments, such as the theory of naturalconscience, his anti-voluntarism, and his belief in the immateriality of the soul, Trotter showed that he oftenmisinterpreted John Locke＇s principles, especially those concerning his moral epistemology.
基金Supported by the National Natural Science Foundation of China(Grant No.12171361)the Humanity and Social Science Youth foundation of Ministry of Education(Grant No.20YJC790174)。
文摘This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.
基金supported by an NSERC granta startup fund of University of Alberta
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
