The Doob decomposition theorem, proved by and named for Joseph L. Doob, is a result in the discrete-time theory of stochastic processes. It states that every adapted, integrable stochastic process can be uniquely written as the sum of a martingale and a predictable process that starts at zero.
Facts
Statementthe Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero. 1 Classification
Statement Form Sources
1. Doob decomposition theorem - Wikipedia
Lead section
the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero.
Citations section
Doob (1953), see (Doob 1990, pp. 296-298)
Lead section, statement-form reference
In the theory of stochastic processes in discrete time, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.