Basic study on immigration super processes and catalytic super diffusions

我们构造了一个数学模型（比如说一个随机过程），该模型能够描述状态根据位置的好坏而改变其分支机制，并研究了该过程的唯一性和规律性。基于此，我们提出了一个随机模型的免疫反应对癌细胞，通过考虑细胞毒性效应。分析的结果表明，该模型所揭示的局部消光特性在应用上是极其重要的，因为该特性恰好对应于效应子所提供的效应将癌细胞从组织中驱逐出去的情况。

We constructed a mathematical model (say a stochastic process) that is able to describe the status changing its branching mechanism according to whether the circumstance is good or not dependent on the location, and investigated the uniqueness and regularity of the process. On this account, based on the process we proposed a random model for immune response against the cancer cells, by taking cytotoxicity via effectors into consideration. As a result of analysis, we found that the local extinction revealed by the model is of extreme importance on an applicational basis, because the property just corresponds to the situation that effects provided by the effectors expel cancer cells from the tissue.