Prophetentheorie

In the works "Semiamarts and Finite Values" (1977) and "On Semiamarts, Amarts, and Processes with Finite Value" (1978), U. Krengel and L. Sucheston provided interesting results for "Semiamarts," which are generalizations of martingales. Within this rather theoretical framework, they proved that the expected value E sup Xn for stochastically independent random variables Xn, or for "arithmetic" means, can be estimated by a multiple of the value sup E(T) T stopping time. They interpreted this result as an estimate of the disadvantage a player (who can only use stopping rules) has against an all-knowing (but not all-powerful) opponent. Shortly thereafter, Krengel and Sucheston referred to this opponent, who knows the entire future, as the Prophet, a term that has been adopted by all subsequent authors. In rapid succession.