Vtyjkyuk

The following textbooks (line read in Kiefer Sutherland's voice) appear to have overlaps, as is expected :

• David Williams: Probability with Martingales




• Rogers and Williams' two volumes: Diffusions, Markov Processes and Martingales




• Oksendal: Stochastic Differential Equations,




• Karatzas and Shreve: Brownian Motion and Stochastic Calculus




• Revuz and Yor: Continuous Martingales and Brownian Motion




• Bobrowski: Functional Analysis for Probability and Stochastic Processes

Some of the overlaps include Girsanov's Theorem, Radon-Nikodym derivative and Feynman-Kac formula.

In general, what might one, who self-studies and hopes to do a PhD in these eventually ($liminf$), do about these?

What about in the specific case of these textbooks, not limited to these topics?

1. Skip them after learning once.


2. Study them every time regardless.


3. Look through quickly to see if there's anything new to study


4. Study intensely the first time, and continue to do so the second time onward but with less intensity.


5. Study again if the topic appears to be presented with different proof or in a different context.


6. (more of a continuation of #5) If the topic has different uses but similar proof and context, the former is worth studying, but the latter isn't.


7. Some combination of above


8. Something else