Doob, Ignatov and optional skipping.
Let \(\xi_1,\xi_2,\dots\) be an i.i.d. sequence of random variables, taking values in a measurable space with common distribution \(F\). The authors describe a general set of conditions on a sequence of stopping times \(\tau_1,\tau_2,\dots\), not depending on \(F\), which guarantee that \(\xi_{\tau_1},\xi_{\tau_2}.\dots\) be i.i.d. with common distribution \(F\). This work is motivated by theorems of \textit{J. L. Doob} [Ann. Math. (2) 37, 363--367 (1936; Zbl 0013.40802)] and \textit{Z. Ignatov} [God. Sofij. Univ., Fak. Mat. Mekh. 71 (1976/1977), Part II, 79--94 (1986; Zbl 0619.60052)]. The authors unify and extend aspects of both.
scientific article; zbMATH DE number 1906105
scientific article