n*********3
发帖数: 21 | 1 WHY w**2-t is martingale, please help to prove. Many thanks |
o****e
发帖数: 80 | 2 use ito lemma,
df = 2wdw
no drift term, so martingale
【在 n*********3 的大作中提到】
: WHY w**2-t is martingale, please help to prove. Many thanks
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n*********3
发帖数: 21 | |
b**********5
发帖数: 51 | 4 E(w**2-t)=E(w**2)-E(t)=t-t=0, so martingale. |
J******d
发帖数: 506 | 5 This is NOT a proof.
【在 b**********5 的大作中提到】
: E(w**2-t)=E(w**2)-E(t)=t-t=0, so martingale.
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k***p
发帖数: 115 | 6 For any s>t.
E (w_s^2-s|F_t)
=E((w_s-w_t)^2+2(w_s-w_t)w_t +w_t^2 -s|F_t)
=E(w_s-w_t)^2+w_t^2-s
=s-t+w_t^2-s
=w_t^2-t
【在 n*********3 的大作中提到】
: WHY w**2-t is martingale, please help to prove. Many thanks
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j*****4
发帖数: 292 | 7 do you use E(W_s^2|F_t)=W_s^2?
I think it should be
W_s^2-s=(W_s-W_t+W_t)^2-s+t-t
【在 k***p 的大作中提到】
: For any s>t.
: E (w_s^2-s|F_t)
: =E((w_s-w_t)^2+2(w_s-w_t)w_t +w_t^2 -s|F_t)
: =E(w_s-w_t)^2+w_t^2-s
: =s-t+w_t^2-s
: =w_t^2-t
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k***p
发帖数: 115 | 8 sorry, made a mistake.corrected
【在 j*****4 的大作中提到】
: do you use E(W_s^2|F_t)=W_s^2?
: I think it should be
: W_s^2-s=(W_s-W_t+W_t)^2-s+t-t
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