slides_7_converge

# 14 when w n n 12 n converges in probability to c we

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When W n : n 1,2,..., n converges in probability to c we also say that c is the probability limit of W n . Sometimes we get sloppy and refer to W n , but convergence in probability is about sequences of random variables. More notation. We write plim n W n c (and often drop “ n ”) or W n p c 15
There is an important notation for the special case W n p 0. As we will see later, to facilitate the alebra of asymptotic theory, it is handy to write W n o p 1 (read “little oh pee one”) when W n p 0. We will see in Section 4 where the “1” in parentheses comes from. The definition extends immediately to the idea of convergence in probability to a random variable rather than a constant (although it comes up less often). We require, for all 0, P | W n W | 0 as n . 16

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