Definition
Let (Ω, F, P) be a probability space; let F∗ = { Ft | t ≥ 0 } be a filtration of F; let X : [0, +∞) × Ω → S be an F∗-adapted stochastic process. Then X is called an F∗-local martingale if there exists a sequence of F∗-stopping times τk : Ω → [0, +∞) such that
- the τk are almost surely increasing: P = 1;
- the τk diverge almost surely: P = 1;
- the stopped process
- is an F∗-martingale for every k.
Read more about this topic: Local Martingale
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