👉 In probability theory and statistics, a martingale is an abstract mathematical construction which is a sequence of random variables (or processes) that converge in distribution to a common limit. It is often used as a tool for studying the behavior of stochastic processes such as random walks or Brownian motion. A martingale does not necessarily have a finite expectation value, and it is necessary that the process be adapted to a filtration (a sequence of Borel probability measures on the space), so that its
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What is the definition of Martingale? 🙋
👉 A martingale is a stochastic process in which each step of the process has an expected value equal to zero. This means that if the process $X_t$ is defined as a sequence of random variables $(X_t)$, then for any stopping time $\tau$, we have: $$E\left(X_{\tau}\right) = 0.$$ This property is crucial in probability theory and stochastic calculus, where it allows us to study the behavior of a process over time. The
