Mathematical Sciences: Branching Measure-Valued Stochastic Processes and Related Topics

马尔可夫过程理论的研究主要集中在函数空间中的分支测度值过程和相关过程。分支的一般形式，超扩散的路径性质与非线性微分方程的正解之间的关系以及具有相互作用部分的“随机云”的建模是研究的主要目标。测量值分支过程自20世纪60年代末开始研究，并在过去五年中引起了广泛的关注。这是一类了不起的过程，它为研究空间分布的人口提供了一种工具。它们还使概率论和偏微分方程理论之间的重要联系得以扩展。

Investigations in the theory of Markov processes are to be done with concentration on branching measure-valued processes and related processes in spaces of functions. The general form of branching, the relationship between path properties of superdiffusions and positive solutions of nonlinear differential equations and modeling of "a random cloud" with interacting parts are among the principal objectives of the investigation. Measure-valued branching processes have been studied since the late 1960s and have attracted a great deal of attention during the last five years. This is a remarkable class of processes, which provide a tool for the investigation of spatially distributed populations. They also make it possible to extend important connections between probability theory and the theory of partial differential equations.