Local continuous martingale

Question

Hi,

This is a relatively simple result with a simple proof. However, there are 2 things I don't understand:

1. Why is M a brownian motion?
2. How is I calculated ("Thus, we get...")?

Any insight would be helpful :)

Thanks!

Answer 1

Hi,

For the first one, this is Dambis, Dubbins Schwartz Theorem

For the second one, we need more context but this is (if true) a bit too fast IMO for a proof.

By the way, from where does this come from ?

Regards