Mathematical Sciences: Markov Processes

首席研究员将研究大系统在适当时空尺度下的水动力或宏观极限行为问题。这个问题在经典和随机环境中都很重要。主要研究者期望使用大偏差理论（空间和时间）的技术来研究这一现象。在过去的几年里，首席研究员与其他人一起开发了在这种情况下有效利用狄利克雷形式的技术。这些技术将被修改，以涵盖这类问题的大类。这些问题的解决方案将影响概率和数学物理。

The principal investigator will study the problem of hydrodynamical or macroscopic limiting bahaviour of large systems under suitable scaling of space and time. This problem is important both in the classical as well as the stochastic context. The principal investigator expects to use techniques from large deviations theory (spatial as well as temporal) to study this phenomenon. In the last few years the principal investigator with others has developed techniques that make effective use of Dirichlet forms in ths context. These techniques will be modified to cover large classes of such problems. Solutions of these problems will impact both probability and mathematical physics.