Stochastic differential equations in Hilbert spaces: solutions and asymptotic behavior

无限维空间中的随机微分方程在量子力学中得到了广泛的应用：作为开放量子系统的有效描述，作为坍缩理论和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，这在所有应用中都很有趣。我们希望特别着重于：1。特定方程解的时间演化分析，具有重要的物理意义。如果可能，将计算通解。解的渐近性的分析。描述自发波函数坍缩的随机微分方程的相对论推广。

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.