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DOOBS DECOMPOSITION AND MARTINGALES
Could someone help me prove equation 1:For any adapted process {x(t)} and any 0<=s<=t<=TEp[z(t)x(t)|F(s)] -------------------- = Eq[x(t)|F(s)] [1]Ep[z(t)|F(s)]where z(t) is the likelihood ratio process defined as Ep[q/p|F(t)] F is a filtration processand z(t) is a positive P-martingaleMany thanks
Last edited by sunil100 on November 12th, 2003, 11:00 pm, edited 1 time in total.
DOOBS DECOMPOSITION AND MARTINGALES
I did have a go at this, using tower's law....but cam unstuck. fyi. tower's law states:Ep[Ep(x|G)|F]=Ep[x|F]