Mathematical Sciences: Topics in Markov Processes

研究人员将继续他的工作在一般领域的马尔可夫过程。最近，研究人员与合作者开发了一组可逆变换的马尔可夫过程，保留了收集过多的功能的过程。这个集合是一个对称群，可以用来构造马尔可夫函数，当与马尔可夫过程组合时，会产生一个新的马尔可夫过程（如果速度被纠正）。研究人员将继续研究马尔可夫过程的概率结构，该过程被编码在该组的代数结构中。这项研究将产生一个新的代数技术分析马尔可夫过程的结构。研究人员将继续他的工作在一般领域的马尔可夫过程。马尔可夫过程是一种概率模型，其特征在于为了描述过程的未来，只需知道过程的当前状态（而不是过去）。这个模型已经成功地应用于从经济学到化学和物理学的各个领域。研究者将使用数学的另一个分支，即代数，来研究这种过程的结构。

The investigator will continue his work in the general area of Markov processes. Recently, the investigator with a collaborator developed a set of invertible transformations of a Markov process which preserved the collection of excessive functions of the process. This collection is a symmetry group which can be used to construct Markov functions, which when composed with Markov processes result in a new Markov process (if the speed is corrected). The investigator will continue to study the probabilistic structure of the Markov process which is coded in the algebraic structure of the group. This study will yield a new algebraic technique for analyzing the structure of Markov processes. The investigator will continue his work in the general area of Markov processes. A Markov process is a probabilistic model which is characterized by the statement that in order to characterize the future of the process, it is enough to know the current state (and not the past) of the process. This model has been used successfully in fields as diverse as economics to chemistry and physics. The investigator will be studying the structure of such processes by using a different branch of mathematics, i.e. algebra.