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A convex function of a martingale is a submartingale, by Jensen's inequality. For example, the square of the gambler's fortune in the fair coin game is a submartingale (which also follows from the fact that X n 2 − n is a martingale). Similarly, a concave function of a martingale is a supermartingale.
Schematic view of the bow of a ship, showing: A the martingale stay, B the dolphin striker and C the bobstay. A dolphin striker (an older term for a martingale boom or simply a martingale; sometimes called a striker) is a small vertical or near vertical ancillary spar spanning between the bowsprit and martingale thereby redirecting the tension in the forward end of the martingale slightly more ...
In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose {: =,,,, …} is a martingale (or super-martingale) and
Schematic view of the bow of a ship, showing: A the martingale stay, B the dolphin striker and C the bobstay. Bows of HMS Victory: three parallel bobstays, separate dolphin-striker with martingale stays. A bobstay is a part of the rigging of a sailing boat or ship. Its purpose is to counteract the upward tension on the bowsprit from the jibs ...
The name comes from a martingale strap used in the horse tack to restrict the movements of the horse's head; [4] another theory suggests that the martingale coat originated in the 15th–16th centuries when a design of a man's martingale breeches [6] included a flap between the legs buttoned to the belt in the back.
A flat belt has an effective angle of =. The material of a V-belt or multi-V serpentine belt tends to wedge into the mating groove in a pulley as the load increases, improving torque transmission. [6] For the same power transmission, a V-belt requires less tension than a flat belt, increasing bearing life. [5]
The condition that the martingale is bounded is essential; for example, an unbiased random walk is a martingale but does not converge. As intuition, there are two reasons why a sequence may fail to converge. It may go off to infinity, or it may oscillate. The boundedness condition prevents the former from happening.
In the mathematical theory of probability, a Doob martingale (named after Joseph L. Doob, [1] also known as a Levy martingale) is a stochastic process that approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random ...
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