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:
“Reporters for tabloid newspapers beat a path to the park entrance each summer when the national convention of nudists is held, but the cults requirement that visitors disrobe is an obstacle to complete coverage of nudist news. Local residents interested in the nudist movement but as yet unwilling to affiliate make observations from rowboats in Great Egg Harbor River.”
—For the State of New Jersey, U.S. public relief program (1935-1943)