Talk:Local martingale

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[edit] F a flitration of itself?

The text currently says that "F = { ... } is a filtration of F". Should those Fs be different? Which one is referred to in the rest of the article? LachlanA (talk) 22:01, 2 June 2008 (UTC)

F is a σ-algebra. For each t, F_t is a σ-subalgebra of F. The collection of all such F_t's is denoted F_∗. I like to think of the “∗” as saying “is a function of t, but we're not saying any particular value of t”. In other words, F and each F_t are σ-algebras, but the filtration F_∗ is a collection of σ-algebras. The rest of the article uses exactly this notation. Sullivan.t.j (talk) 10:25, 3 June 2008 (UTC)