Martingale Convergence Theorem

The Martingale Convergence Theorem states that in probability theory, a certain type of mathematical sequence (called a martingale) will eventually stabilize or converge to a specific value, given that it is bounded or meets certain conditions. Imagine a fair game where you bet on a coin toss; over time, your winnings might fluctuate, but if you keep playing under fair rules, your average winnings will settle around a target value. This theorem helps in understanding behaviors of systems over time, particularly in finance and statistics, ensuring that we can predict long-term outcomes from short-term randomness.