In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under...

finite time. Stopping times occur in decision theory, and the optional stopping theorem is an important result in this context. Stopping times are also...

it implies (6). For convenience (see the proof below using the optional stopping theorem) and to specify the relation of the sequence (Xn)n∈ N {\displaystyle...

martingale leads to a series of important theorems, including, for example, the optional stopping theorem which states that, under certain conditions...

decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal...

uniformly integrable), and Doob's optional stopping theorem might not be applicable to the martingale M unless the stopping time has a finite expectation...

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

optimal time to exercise. Halting problem Markov decision process Optional stopping theorem Prophet inequality Stochastic control Sequential analysis Chow...

decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal...

the size of one's bankroll or line of credit, is proven by the optional stopping theorem. However, without these limits, the martingale betting strategy...

representation theorem (probability theory) Maxwell's theorem (probability theory) Optional stopping theorem (probability theory) Poisson limit theorem (probability)...

time is just E [ X T ] {\displaystyle E[X_{T}]} , which by the optional stopping theorem is E [ X T ] = E [ X 0 ] = p − q p + q {\displaystyle E[X_{T}]=E[X_{0}]={\frac...

probability theory, Kramkov's optional decomposition theorem (or just optional decomposition theorem) is a mathematical theorem on the decomposition of a...

{\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...

decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal...

Markov process Martingale Doob martingale Optional stopping theorem Martingale representation theorem Azuma's inequality Wald's equation Poisson process...

martingale). The results then follow as a consequence of Doob's optional stopping theorem and Ville's inequality. We already implicitly used product e-variables...

analysis Optimal matching Optimal stopping Optimality criterion Optimistic knowledge gradient Optional stopping theorem Order of a kernel Order of integration...

decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal...

Doob's martingale convergence theorems Doob's martingale inequality Doob–Meyer decomposition theorem Optional stopping theorem Doob, Joseph Leo, Community...

iterated logarithm / (S:R) Maximal ergodic theorem / (S:R) Op (statistics) / (S:R) Optional stopping theorem / (FS:R) Stationary process / (SU:R) Stochastic...

say that the stopping time or the total stopping time, respectively, is infinite. The Collatz conjecture asserts that the total stopping time of every...

Arrow's theorem do not directly apply to them. Some ranked voting systems require the voter rank a set number of candidates. Others, such as optional preferential...

a sequential hypothesis testing, or optional stopping, for the fairness of the coin. In general, optional stopping changes how p-value is calculated. Suppose...

closed under optional stopping, localization, change of time and absolutely continuous change of probability measure (see Girsanov's Theorem). If X is an...

Model-based testing is an application of model-based design for designing and optionally also executing artifacts to perform software testing or system testing...

complicated example of those, using a commonly cited example called the optional stopping problem. Example 1 – simple version Suppose I tell you that I tossed...

of control usually returns (subroutines, coroutines, and continuations) Stopping the program, preventing any further execution (unconditional halt) A label...

consistency of configuration data over availability/performance (see CAP theorem). The IMM service follows the three-tier OpenSAF "Service Director" framework...

observed. With optional stopping, there are even rarer events that are difficult to account for, i.e. not triggering the optional stopping rule, and collecting...