Andrei Andreyevich Markov

1. Markov Property

The principle that the future state depends only on the current state, not the past.

$$ P(X_{n+1} = x \mid X_1 = x_1, \dots, X_n = x_n) = P(X_{n+1} = x \mid X_n = x_n) $$

2. Markov Inequality

A fundamental bound in probability theory.

$$ P(X \ge a) \le \frac{E[X]}{a} $$