Statement of The Theorems
In the following, (Ω, F, F∗, P), F∗ = (Ft)t≥0, will be a filtered probability space and N : [0, +∞) × Ω → R will be a right-continuous supermartingale with respect to the filtration F∗; in other words, for all 0 ≤ s ≤ t < +∞,
Read more about this topic: Doob's Martingale Convergence Theorems
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“Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.”
—Robert Benchley (1889–1945)