sonxi111
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Martingale betting strategy analysis
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![Typed math problem: i.i.d. random variables pi_1 to pi_n with distribution function F and density f; binomial process Z_n(t) = sum of indicators; show M_n(t) = Z_n(t) minus integral of [n - Z_n(s)] f(s)/(1 - F(s)) ds is a martingale; then Excel steps for n=20 and n=50 defining v_n and w_n.](/data/attachments/11/11655-d889af6d4d451288badcc9e170f06db0.jpg?hash=2ImvbU1FEo)
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sonxi111
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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?
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?
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