Is Martingale the Key to Success? (Attached File)

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question in attached file.
thanks in advance
 

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the lecture told us to think about that this way:
if 0<t1<t2<---<tk<t
1. first, what is the conditional probability of z_n(t)-z_n(tk) given that z_n(t1),z_n(t2)...z_n(tk) ?
2. is this process z_n(t) Markovian?