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- W2079307214 abstract "Let $E$ be a locally compact Hausdorff space with countable basis and let $(X_i)_{iinmathbb{N}}$ be a family of random elements on $E$ with $(1/n) sum^n_{i=1} mathscr{L}(X_i) Rightarrow^v mu (n rightarrow infty)$ for a measure $mu$ with $|mu| leq 1$. Conditions are derived under which $mathscr{L} ((1/n) sum^n_{i=1} delta_{Xi}) Rightarrow^w delta_mu(n rightarrow infty)$, where $delta_x$ denotes the Dirac measure at $x$. The proof being based on Stein's method, there are generalisastions that allow for weak dependence between the $X_i$'s. As examples, a dissociated family and an immigration-death process are considered. The latter illustrates the possible applications in proving convergence of stochastic processes." @default.
- W2079307214 created "2016-06-24" @default.
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- W2079307214 date "1995-01-01" @default.
- W2079307214 modified "2023-09-27" @default.
- W2079307214 title "A Weak Law of Large Numbers for Empirical Measures via Stein's Method" @default.
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- W2079307214 doi "https://doi.org/10.1214/aop/1176988389" @default.
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