New development of excursion theory for Markov processes

本文从以下四个方面对马氏过程的游程理论作了新的发展。(1)处罚问题，我。例如，用加权和正规化变换的马氏过程的极限问题。(2)扩散过程在包含边界跳跃的区间上的延拓。(3)漂移测度的等价性与惩罚问题的统一的σ有限测度。(4)离散Tsirelson方程的广义问题，特别是那些在紧群中取值的问题，以及根据道路着色演化的马尔可夫链问题。

I have made new developments of excursion theory for Markov processes from the following four viewpoints.(1) The penalisation problems, i. e., the limit problems of Markov processes transformed by weight and normalization.(2) Extension of diffusion process on intervals which involves jumps from the boundaries.(3) Extremality of excursion measures and the sigma-finite measures unifying penalisation problems.(4) Generalized problems of discrete Tsirelson equations, in particular, those taking values in compact groups, and those of Markov chains evolving according to a road coloring.