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right-continuous martingale

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  • Martingale (probability theory) — For the martingale betting strategy , see martingale (betting system). Stopped Brownian motion is an example of a martingale. It can be used to model an even coin toss betting game with the possibility of bankruptcy. In probability theory, a… …   Wikipedia

  • Doob's martingale convergence theorems — In mathematics specifically, in stochastic analysis Doob s martingale convergence theorems are a collection of results on the long time limits of supermartingales, named after the American mathematician Joseph Leo Doob. Contents 1 Statement of… …   Wikipedia

  • Doob's martingale inequality — In mathematics, Doob s martingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process exceeds any given value over a given interval of time. As the name suggests, the result… …   Wikipedia

  • Itō calculus — Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations.The central… …   Wikipedia

  • Wiener process — In mathematics, the Wiener process is a continuous time stochastic process named in honor of Norbert Wiener. It is often called Brownian motion, after Robert Brown. It is one of the best known Lévy processes (càdlàg stochastic processes with… …   Wikipedia

  • Quadratic variation — In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and martingales. Quadratic variation is just one kind of variation of a process. Definition Suppose that X t is a real valued stochastic… …   Wikipedia

  • Brownian motion — This article is about the physical phenomenon; for the stochastic process, see Wiener process. For the sports team, see Brownian Motion (Ultimate). For the mobility model, see Random walk. Brownian motion (named after the botanist Robert Brown)… …   Wikipedia

  • probability theory — Math., Statistics. the theory of analyzing and making statements concerning the probability of the occurrence of uncertain events. Cf. probability (def. 4). [1830 40] * * * Branch of mathematics that deals with analysis of random events.… …   Universalium

  • Black–Scholes — The Black–Scholes model (pronounced /ˌblæk ˈʃoʊlz/[1]) is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives the price of European …   Wikipedia

  • Hardy space — In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923), who named them after G. H. Hardy, because of the… …   Wikipedia

  • Central limit theorem — This figure demonstrates the central limit theorem. The sample means are generated using a random number generator, which draws numbers between 1 and 100 from a uniform probability distribution. It illustrates that increasing sample sizes result… …   Wikipedia

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