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:
“The improved American highway system ... isolated the American-in-transit. On his speedway ... he had no contact with the towns which he by-passed. If he stopped for food or gas, he was served no local fare or local fuel, but had one of Howard Johnson’s nationally branded ice cream flavors, and so many gallons of Exxon. This vast ocean of superhighways was nearly as free of culture as the sea traversed by the Mayflower Pilgrims.”
—Daniel J. Boorstin (b. 1914)