Reflection Principle And First Passage Time Of Special Fuzzy Process

Credibility theory is a branch of mathematics for studying the behavior of fuzzy phenomena. Fuzzy process is a type of uncertain process and it is described by membership function. Liu process is a special fuzzy process. Liu process has been widely applied in the dynamic fuzzy phenomenon. Brownian motion is very important in stochastic process. Liu process, which corresponds to Brownian motion, plays an important role in describing dynamic fuzzy events. However the theory of fuzzy process is not perfect, so further research is deeded.Based on credibility theory and fuzzy process, reflection principle and first passage time of a special Liu Process were proved in this paper. At the same time, we obtained the credibility of first passage time. Furthermore we discussed the credibility of Liu process arrives a before arrives b and Liu process absorbed at a value. These results provide a theoretical foundation for the further application of Liu process in financial field.