Theory of Probability and Mathematical Statistics
Convergence in Distribution for Randomly Stopped Random Fields
D. Silvestrov
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Abstract: Let $\XX$ and $\YY$ be two complete, separable, metric spaces, $\xi_\e(x), x \in \XX$ and $\nu_\e$ be, for every $\e \in [0, 1]$, respectively, a random field taking values in space $\YY$ and a random variable taking values in space $\XX$. We present general conditions for convergence in distribution for random variables $\xi_\e(\nu_\e)$ that is the conditions insuring holding of relation, $\xi_\e(\nu_\e) \stackrel{\dd}{\longrightarrow} \xi_0(\nu_0)$ as $\e \to 0$.
Keywords: Random field, random stopping, convergence in distribution
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