Mathematical Sciences: Studies on Markov Chains and Branching Processes

研究将继续在非线性过滤、马尔可夫链和分支过程等领域进行。在非线性滤波中，将研究近似法，并对各种近似法进行比较。对于一般状态空间上的马尔可夫链，需要寻求转移函数的一致和渐近正态估计。还将调查超临界分支过程中种群估计的较大偏差。将研究如何在接收到信号时区分原始信号和干扰。此外，还将尝试估计某些类型的随机演变过程的概率结构。

Research will continue in the areas of nonlinear filtering, Markov chains, and branching processes. In nonlinear filtering, approximations will be studied and comparisons will be made between various approximations. For Markov chains on a general state space, consistent and asymptotically normal estimates of the transition function are to be sought. Large deviations of the estimates of the population in a supercritical branching process will also be investigated. Research will be done on distinguishing between the original signal and interference when a signal has been received. In addition, attempts will be made to estimate the probability structure of certain types of randomly evolving processes.