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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; in particular, every local martingale that is bounded from below is a supermartingale, and every local martingale that is bounded from above is a submartingale; 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. ==Definition== Let (Ω, ''F'', P) be a probability space; let ''F''∗ = be a filtration of ''F''; let X : = 1; * the stopped process :: : is an ''F''∗-martingale for every ''k''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「local martingale」の詳細全文を読む スポンサード リンク
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