Stochastic differential equations in Hilbert spaces: solutions and asymptotic behavior

希尔伯特空间中的随机微分方程：解和渐近行为

• 批准号: 31294094
• 负责人: Professor Dr. Detlef Dürr (†)
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/31294094?language=en
• 关键词: Stochastic; differential; equations; Hilbert; spaces

Stochastic differential equations in infinite dimensional spaces have been used widely in Quantum Mechanics: as effective descriptions of open quantum systems, as fundamental equations for collapse theories, for continuous measurement theory.Recently we began to study the long time behavior of such equations, which is of interest in all applications. In particular we wish to focus on:1. Analysis of the time evolution of solutions of specific equations, which are physically significant. When possible, the general solution will be computed.2. Analysis of the asymptotic behavior of the solutions.3. Relativistic generalization of stochastic differential equations describing spontaneous wave function collapse.

无限维空间中的随机微分方程在量子力学中有着广泛的应用：作为开放量子系统的有效描述，作为坍缩理论的基本方程，连续测量理论的基本方程，最近我们开始研究这类方程的长时间行为，这在所有的应用中都是令人感兴趣的。我们希望特别关注：1。分析特定方程的解的时间演化，这在物理上是有意义的。在可能的情况下，将计算一般解.分析解的渐近性态.描述自发波函数坍缩的随机微分方程的相对论推广。