Since the seminal work of Wiener(Am J Math 60:897-936,1938),chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations.Yet its complexity for systems subject ...Since the seminal work of Wiener(Am J Math 60:897-936,1938),chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations.Yet its complexity for systems subject to the white noise remains significant.The issue appears due to the fact that the random increments generated by the Brownian motion result in a growing set of random variables with respect to which the process could be measured.In order to cope with this high dimensionality,we present a novel transformation of stochastic processes driven by the white noise.In particular,we show that under suitable assumptions,the diffusion arising from white noise can be cast into a logarithmic gradient induced by the measure of the process.Through this transformation,the resulting equation describes a stochastic process whose randomness depends only on the initial condition.Therefore,the stochasticity of the transformed system lives in the initial condition and it can be treated conveniently with chaos expansion tools.展开更多
In our previous paper [1], we proposed a non-standardization of the concept of convolution in order to construct an extended Wiener measure using nonstandard analysis by E. Nelson [2]. In this paper, we consider Ito’...In our previous paper [1], we proposed a non-standardization of the concept of convolution in order to construct an extended Wiener measure using nonstandard analysis by E. Nelson [2]. In this paper, we consider Ito’s integral with respect to the extended Wiener measure and extend Ito’s formula for Ito’s process. Because of doing the extension of Ito’s formula, we could treat stochastic differential equations in the sense of nonstandard analysis. In this framework, we need the nonstandardization of convolution again. It was not yet proved in the last paper, therefore we shall provide the proof.展开更多
氧化铟锡(Indium Tin Oxide, ITO)靶材是屏幕显示器、光伏电池、功能玻璃等领域的关键原材料之一,已朝着大尺寸(长度至少600 mm)、高密度、低电阻率和高使用率的方向发展。本文介绍了高性能ITO靶材的技术特征,分析了大尺寸ITO靶材的需...氧化铟锡(Indium Tin Oxide, ITO)靶材是屏幕显示器、光伏电池、功能玻璃等领域的关键原材料之一,已朝着大尺寸(长度至少600 mm)、高密度、低电阻率和高使用率的方向发展。本文介绍了高性能ITO靶材的技术特征,分析了大尺寸ITO靶材的需求和镀膜优势,总结了大尺寸ITO靶材的成型、烧结工艺及其研究应用现状,最后提出了制备大尺寸ITO靶材的研究方向。展开更多
基金the funding provided by the Swiss National Science Foundation under the Grant No.174060.
文摘Since the seminal work of Wiener(Am J Math 60:897-936,1938),chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations.Yet its complexity for systems subject to the white noise remains significant.The issue appears due to the fact that the random increments generated by the Brownian motion result in a growing set of random variables with respect to which the process could be measured.In order to cope with this high dimensionality,we present a novel transformation of stochastic processes driven by the white noise.In particular,we show that under suitable assumptions,the diffusion arising from white noise can be cast into a logarithmic gradient induced by the measure of the process.Through this transformation,the resulting equation describes a stochastic process whose randomness depends only on the initial condition.Therefore,the stochasticity of the transformed system lives in the initial condition and it can be treated conveniently with chaos expansion tools.
文摘In our previous paper [1], we proposed a non-standardization of the concept of convolution in order to construct an extended Wiener measure using nonstandard analysis by E. Nelson [2]. In this paper, we consider Ito’s integral with respect to the extended Wiener measure and extend Ito’s formula for Ito’s process. Because of doing the extension of Ito’s formula, we could treat stochastic differential equations in the sense of nonstandard analysis. In this framework, we need the nonstandardization of convolution again. It was not yet proved in the last paper, therefore we shall provide the proof.
文摘氧化铟锡(Indium Tin Oxide, ITO)靶材是屏幕显示器、光伏电池、功能玻璃等领域的关键原材料之一,已朝着大尺寸(长度至少600 mm)、高密度、低电阻率和高使用率的方向发展。本文介绍了高性能ITO靶材的技术特征,分析了大尺寸ITO靶材的需求和镀膜优势,总结了大尺寸ITO靶材的成型、烧结工艺及其研究应用现状,最后提出了制备大尺寸ITO靶材的研究方向。
