论文标题
时空随机演算和白噪声
Space-time stochastic calculus and white noise
论文作者
论文摘要
在本文的第一部分中，我将最初对随机分析的兴趣和书写随机微分方程的撰写提供了历史背景。这本书的第一版由施普林格于1985年出版，并得到了卡特里奥娜·伯恩（Catriona Byrne）的高度赞赏。在第二部分中，我提出了通过由时空布朗尼板驱动的随机部分微分方程（SPDE）来模拟系统动力学的动机。接下来是对时间空间白噪声和hida-malliavin演算的简要调查，这是研究此类方程的有用工具。作为例证，我使用白噪声计算来找到SPDE的明确解决方案，该解决方案描述了受时间空间白噪声的环境中人群的增长。
In the first part of this paper I give the historical background to my initial interest in stochastic analysis and to the writing of my book Stochastic Differential Equations. The first edition of this book was published by Springer in 1985, with the highly appreciated support of Catriona Byrne. In the second part I present a motivation for modelling the dynamics of a system subject to a noise by means of a stochastic partial differential equation (SPDE) driven by a time-space Brownian sheet. This is followed by a brief survey of time-space white noise and Hida-Malliavin calculus, which are useful tools for studying such equations. As an illustration I apply white noise calculus to find an explicit solution of an SPDE describing population growth in an environment subject to time-space white noise.
