Martingale theory

model in probability theory, used in gambling

stochastic process generalizing Brownian motion

martingale's expected value at a stopping time equals its initial expected value

inequality applying to (sub-)martingales

In probability theory, a real-valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and a càdlàg adapted finite-variation process. Semimartingales are "good integrators", forming the largest class of processes with respect to which the Itô integral and the Stratonovich integral can be defined.

mathematical concept

probabilistic inequality applying to martingales with bounded differences

mathematical construction of a martingale (with respect to a given filtration) approximating a given random variable; the evolving sequence of best approximations to the random variable based on information accumulated up to a certain time

kind of differential equation

stochastic process satisfying the localized martingale property: i.e. such that there exists a sequence of stopping times, almost surely increasing and almost surely diverging, such that the corresponding stopped processes are martingales