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- Brownian motion
- integral of Brownian path
- the L log L-inequality of Hardy and Littlewood
- optimal stopping (time)
- the principle of smooth fit
- the maximality principle
- Stephan's problem with moving boundary
- Itô-Tanaka's formula
- Burkholder-Gundy's inequality
- Doob's maximal inequality
- Doob's optional sampling theorem
- local time