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local martingale

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  • Local martingale — In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; however, in general a local… …   Wikipedia

  • 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

  • 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

  • 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

  • Semimartingale — In probability theory, a real valued process X is called a semimartingale if it can be decomposed as the sum of a local martingale and an adapted finite variation process.Semimartingales are good integrators , forming the largest class of… …   Wikipedia

  • Girsanov theorem — In probability theory, the Girsanov theorem tells how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it tells how to convert from the physical measure which… …   Wikipedia

  • Doléans-Dade exponential — In stochastic calculus, the Doléans Dade exponential, Doléans exponential, or stochastic exponential, of a semimartingale X is defined to be the solution to the stochastic differential equation dYt = Yt dXt with initial condition Y0 = 1. The… …   Wikipedia

  • Théorème de Girsanov — Visualisation du théorème de Girsanov Le côté gauche montre un processus de Wiener avec une tendance négative sous la mesure canonique P; sur le côté droit, chaque trajectoire du processus est colorée selon sa vraisemblance sous la mesure… …   Wikipédia en Français

  • Stopping time — Example of a stopping time: a hitting time of Brownian motion In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time) is a specific type of “random time”. The theory of stopping rules and… …   Wikipedia

  • List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

  • Decomposition (disambiguation) — Decomposition may refer to the following: Decomposition, biological process through which organic material is reduced Chemical decomposition or analysis, in chemistry, is the fragmentation of a chemical compound into elements or smaller compounds …   Wikipedia

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