Filtration F(t) for Girsanov's theorem and Martingale Representation Theorem

Dear experts,

I am reading Martingale Representation theorem from Steven Shreve's Stochastic Calculus book 2.

It is understood that Filtration F(t) for Martingale representation theorem is generated by Brownian motion, whereas for Girsanov's theorem filtration F(t) is generated for the Brownian motion.

I am not clear about the difference between the two filtration calculation methods, and also why this is significant for these two theorems.

Can anyone please refer me to any paper or a video which explains this.

I am reading Stochastic Calculus with the help of a Phd. student and my only sources of gaining understanding is forums like these.

Kindly help.
 
You are reading the wrong text if you care about what most people would consider the minutiae of stochastic calculus. Consider checking out Brownian Motion and Stochastic Calculus by Karatzas and Shreve.

Also, I would consider decreasing the frequency of your posts -- one does not learn mathematics by posting on a forum every time they have a question. Sometimes you need to consult multiple different sources, read and reread many times and think hard. The last point is the most important, and no, thinking hard does not mean thinking for 3 hours. I'm not saying you are not already doing this, but learning a subject like stochastic calculus rigorously takes endurance and stubborness. QuantNet is not a substitute for this.
 
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