2
votes
1answer
171 views

What are some good books about martingales?

I'm looking for suggestions for well written books dealing with martingale theory, not necessarily exclusively. I'm also looking for a nice compilation of problems, preferably with answers, on this ...
3
votes
0answers
66 views

Absolute continuity of quadratic variation of continuous local martingales

I am interested to know if there are any simple sufficient conditions on continuous local martingale to have absolutely continuous quadratic variation. In general , we know only that quadratic ...
1
vote
1answer
58 views

Fake Brownian Motion

Does there exist a martingale which has Marginal distributions same as Brownian Motion marginals but the process itself not being Brownian motion? Any references are highly appreciated. Thanks.
1
vote
1answer
1k views

Questions and Solutions in Brownian Motion and Stochastic Calculus?

I am currently studying Brownian Motion and Stochastic Calculus. I believe the best way to understand any subject well is to do as many questions as possible. Unfortunately, I haven't been able to ...
3
votes
2answers
135 views

Is $M^2-[M]$ a local martingale when $M$ is a local martingale?

I've learned that for each continuous local martingale $M$, there's a unique continuous adapted non-decreasing process $[M]$ such that $M^2-[M]$ is a continuous local martingale. For a local ...