[問題] martingale
1.let (ξ_n) be a sequence of iid Bernoulli random variables with generating
n
function M(t)=E[exp(tξ_1)]<∞ fot t≠0 and let X_n=Σξ_i
i=1
prove that the sequence (Z_n) with Z_n=exp(tX_n)/M^n(t) is a martingale.
2.let X and Y be integrable random variables on a probability space (Ω,F,P)
then we can decompose Y into Y=Y_1+Y_2
where Y_1=E[Y∣X] and Y_2=Y-E[X∣Y]
(a) show that Y_2 and X are uncorrelated.
(b)More general, show that Y_2 is uncorrelated with every σ(X)-measurable
random variable.
想了很久解不出來的問題這此請教大家了 感謝
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