of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process...

The Doob–Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique...

groups. Decomposition of time series, a statistical task that deconstructs a time series into several components Doob decomposition theorem of an integrable...

theory) Doob–Dynkin lemma Doob martingale Doob's martingale convergence theorems Doob's martingale inequality Doob–Meyer decomposition theorem Optional...

Dawson–Gärtner theorem (asymptotic analysis) Donsker's theorem (probability theory) Doob decomposition theorem (stochastic processes) Doob's martingale convergence...

uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions...

Donsker's theorem Doob decomposition theorem Doob martingale Doob's martingale convergence theorems Doob's martingale inequality Doob–Meyer decomposition theorem...

variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

{\displaystyle X_{t}} is also a Gaussian process. In other cases, the central limit theorem indicates that X t {\displaystyle X_{t}} will be approximately normally...

Kramkov's optional decomposition theorem (or just optional decomposition theorem) is a mathematical theorem on the decomposition of a positive supermartingale...

Billingsley 1995, Theorem 31.3; Doob 1953, Theorem VII.3.2; Hall & Heyde 1980, Theorem 2.1; Shiryaev 2019, Theorem 7.3.1. Doob 1953, Theorem VII.3.2; Durrett...

variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac...

Brownian motion Doob martingale Doob's martingale convergence theorems Doob's martingale inequality Doob–Meyer decomposition theorem Local martingale...

the Itô isometry can be used. First, the Doob–Meyer decomposition theorem is used to show that a decomposition M2 = N + ⟨M⟩ exists, where N is a martingale...

variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac...

began the systematic study of ergodicity. He gave and proved a decomposition theorem showing that the ergodic measure preserving actions of the real...

Doob, who was then developing new ideas in the theory of stochastic processes. It was there that he derived his famous theorem on the decomposition of...

the formula to semimartingales. Tanaka's formula is the explicit Doob–Meyer decomposition of the submartingale |Bt| into the martingale part (the integral...

variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac...

/ˈbeɪʒən/ BAY-zhən) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence...

his celebrated hyperbolic Dehn surgery theorem. To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important...

in x {\displaystyle x} . Tanaka's formula provides the explicit Doob–Meyer decomposition for the one-dimensional reflecting Brownian motion, ( | B s | )...

J. L. Doob (1953) Stochastic Processes. New York: John Wiley and Sons ISBN 0-471-52369-0. A. A. Markov (1971). "Extension of the limit theorems of probability...

M_{n}=\operatorname {E} {\bigl (}f|\Sigma _{n}{\bigr )}} belongs to martingale-Hp. Doob's maximal inequality implies that martingale-Hp coincides with Lp(Ω, Σ, P)...

including what would later be called the Bing–Nagata–Smirnov metrization theorem. In 1952, Bing showed that the double of a solid Alexander horned sphere...

of operator algebras and field theory and created the Kaplansky density theorem, Kaplansky's game and Kaplansky conjecture. He published more than 150...

Continuous stochastic process / (U:RG) Doob's martingale convergence theorems / (SU:R) Doob–Meyer decomposition theorem / (U:R) Feller-continuous process /...

M\rangle } is a local martingale. Its existence follows from the Doob–Meyer decomposition theorem and, for continuous local martingales, it is the same as the...

In probability theory, the Gillespie algorithm (or the Doob–Gillespie algorithm or stochastic simulation algorithm, the SSA) generates a statistically...