The Truncated Markov Processes Prior to α and the Truncated Markov Processes After α
Tang Rong, Yonghui Huang · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2009
It is proved that the truncated sample path function of a Markov process X(t,ω) prior to α(ω) is still a Markov process if {αt}∈F∞t for every t≥0,and the one after α(ω) is also a Markov process.Moreover,for an arbitrary stochastic process X(t,ω) which may not be a Markov process,it is showed that the σ-algebra Ft prior to t of X(t,ω) is right continuous(i.e.,Ft=∩stFs) and the first hitting time is a stopping time.