Doob-Meyer decomposition theorem
- Doob-Meyer decomposition theorem
The Doob-Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and a continuous increasing process. It is named for J. L. Doob and Paul-André Meyer.
The theorem
If is a continuous submartingale such that the set:(where is a stopping time) is uniformly integrable, then there exists a continuous martingale and a continuous increasing process such that:
almost surely.
The processes and are unique to the point of indistinguishability.
External links
* [http://fa.its.tudelft.nl/seminar/seminar2003_2004/lecture3.pdf The Doob-Meyer decomposition theorem with proof, by Jan van Neerven]
Wikimedia Foundation.
2010.
Look at other dictionaries:
Doob–Meyer decomposition theorem — The Doob–Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and a continuous increasing process. It is named for J. L.… … Wikipedia
Doob decomposition theorem — In the theory of discrete time stochastic processes, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of any submartingale as the sum of a martingale and an increasing predictable… … Wikipedia
Doob — may refer to several things: Joseph Leo Doob, an American mathematician Doob martingale Doob s martingale inequality Doob–Meyer decomposition theorem The Doobie Brothers band A slang for cannabis See also Boob (disambiguation) … Wikipedia
Decomposition (disambiguation) — Decomposition may refer to the following: Decomposition, biological process through which organic material is reduced Chemical decomposition or analysis, in chemistry, is the fragmentation of a chemical compound into elements or smaller compounds … Wikipedia
Joseph Leo Doob — Infobox Scientist name = Joseph Doob image width = 300px caption = Joseph Leo Doob birth date = birth date|1910|2|27|mf=y birth place = Cincinnati, Ohio, U.S. residence = nationality = death date = death date and age|2004|6|7|1910|2|27|mf=y death … Wikipedia
Itō calculus — Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations.The central… … Wikipedia
List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… … Wikipedia
List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… … Wikipedia
Quadratic variation — In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and martingales. Quadratic variation is just one kind of variation of a process. Definition Suppose that X t is a real valued stochastic… … Wikipedia
