👉 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
What is the definition of Martingal? 🙋
👉 In probability theory, a martingale is a sequence of random variables that converges in distribution to a limit. A martingale is not necessarily a sequence of independent random variables, but its convergence in distribution is equivalent to the convergence in law. The term "martingal" comes from the French word "maritime," which means "ship," and "gallant." It refers to the act of crossing a body of water or an ocean. In this context, it can be
