A Note on the Interchangeable Process

  • Hong, Dug-Hun (Department of Statistics, Hyosung Women's University, Kyungbuk, 713-702)
  • 발행 : 1994.12.01

초록

Let ${X_n}$ be conditionally i.i.d. given $g \subset \sigma(X_n, n \geq 1)$. We will prove that $g$ is degenerate if and only if ${X_n, n \geq 1}$ are i.i.d. random variable(r.v.s). As a corollary the Hewitt-Savage zero-one law is obtained using the fact that interchageable process is conditionally i.i.d. given the $\sigma$-algebra of permutable events.

키워드

참고문헌

  1. Transactions American Mathematical Society v.119 Sign-invariant random variables and stochastic process with sign-invariant increments Berman,S.M.
  2. Probability Breiman,L.
  3. Probability theory : independence, interchangeability, martingale (2nd ed.) Chow,Y.S.;Teicher,H.