Every event in the tail σ-algebra of an independent sequence of random variables has probability 0 or 1. Kolmogorov 1928. Examples: convergence of Σ X_n, limsup of X_n/a_n, recurrence/transience of random walks. Reduces asymptotic…
Every event in the tail σ-algebra of an independent sequence of random variables has probability 0 or 1. Kolmogorov 1928. Examples: convergence of Σ X_n, limsup of X_n/a_n, recurrence/transience of random walks. Reduces asymptotic…