In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; however, in general a local martingale is not a martingale, because its expectation can be distorted by large values of small probability. In particular, a driftless diffusion process is a local martingale, but not necessarily a martingale.
Local martingales are essential in stochastic analysis, see Itō calculus, semimartingale, Girsanov theorem.
Read more about Local Martingale: Definition, Martingales Via Local Martingales
Famous quotes containing the word local:
“These native villages are as unchanging as the woman in one of their stories. When she was called before a local justice he asked her age. “I have 45 years.” “But,” said the justice, “you were forty-five when you appeared before me two years ago.” “Señor Judge,” she replied proudly, drawing herself to her full height, “I am not of those who are one thing today and another tomorrow!””
—State of New Mexico, U.S. public relief program (1935-1943)