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
Famous quotes containing the word definition:
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)