Stochastic differential equations in Hilbert spaces: solutions and asymptotic behavior

• Applicant: Professor Dr. Detlef Dürr (†)
• Subject Area: Mathematics
• Term: from 2006 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 31294094

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.

• DFG Programme: Research Grants