ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

1IntroductionSelf-similarMarkoyprocesseson(0,co)wereintroducedbyLamperti[ZI.AnormalMarkovprocessX=(fi,F,R,Xt,ot,p")withstatespace(0,co)iscalledself-similarMarkovprocessoforderorjor>0,ifitstransitionfunctionPt(x,A)satisfiesPt(x,A)=Pa,(a"x,a"A)Vt>9,a>0,x>0,AEB(0,co).Itwasshownin[2]and[11]thateveryself-similarMarkovprocesson(0,co)automaticllyisstronglyMarkovianandhasanicepath",soitisaHuntprocessinthesenseof[1].Thefractalpropertiesoftheprocesseswerestudiedin[6]and[8].TheitoExcursiontheor…