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Statements

Subject Item
dbr:Doob_decomposition_theorem
rdfs:label
Doob decomposition theorem
rdfs:comment
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. The theorem was proved by and is named for Joseph L. Doob. The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem.
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dbc:Articles_containing_proofs dbc:Martingale_theory dbc:Theorems_regarding_stochastic_processes
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n11:Doob_decomposition_theorem?oldid=1045047433&ns=0
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dbr:Optional_stopping_theorem dbr:Mathematical_finance dbr:Almost_surely dbc:Martingale_theory dbr:Adapted_process dbr:Martingale_(probability_theory) dbr:Filtration_(probability_theory) dbr:Snell_envelope dbr:Lebesgue_integration dbr:Option_style dbr:Stopping_time dbr:Uniform_integrability dbr:Risk-neutral_measure dbr:Measurable_function dbr:Conditional_expectation dbr:Euclidean_space dbr:Equivalence_(measure_theory) dbr:Joseph_L._Doob dbr:Σ-finite_measure dbr:Vector_space dbc:Theorems_regarding_stochastic_processes dbr:Empty_sum dbr:Random_walk dbr:Monotonic_function dbr:Doob–Meyer_decomposition_theorem dbr:Stochastic_process dbc:Articles_containing_proofs dbr:Probability_space dbr:Probability_theory dbr:Event_(probability_theory) dbr:Predictable_process dbr:Discounted_cash_flow
dbo:abstract
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. The theorem was proved by and is named for Joseph L. Doob. The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem.
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n11:Doob_decomposition_theorem