2) Martingales Flashcards
(20 cards)
What is a filtration in probability theory
What is a martingale with respect to a filtration
What are submartingales and supermartingale
What is the natural filtration
Fn = σ(Z1, Z2, . . . , Zn), the σ-algebra generated
by Z1, Z2, . . . , Zn
How does expectation behave for martingales, submartingales, and supermartingales
What is Doob decomposition theorem
What is the intuition behind Doob’s Decomposition Theorem
What is a stopping time with respect to a filtration
What are the key properties of stopping times
Describe the proof of the key properties of stopping times
What is a stopped process and how is it defined for a stopping time T
If {Zn ,n≥0} is a martingale, what can be said about the stopped process Yn =ZT∧n
What is the σ-algebra associated with a stopping time τ
What are the key properties of the σ-algebra associated with stopping times
What is Doob’s optional stopping theorem
What are the maximal inequalities for a martingale Xn with Xn ≥0 and E[∣Xn∣ ^p]<∞ for some p≥1
What does the crossing lemma state for a submartingale
What is Doob’s martingale convergence theorem
When is a martingale said to be bounded in L^p
