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- W2069382275 abstract "Let $B_t$ be a two-dimensional Brownian motion and $f(x)$ be a bounded measurable function vanishing outside a compact set. Then $(1/lambda) int^{e^{lambda t}}_0 f(B_s) ds$ converges to const. $ell(M^{-1}(t), 0)$ as $lambda rightarrow infty$, where $ell(t, x)$ and $M(t)$ are the local time and the maximum process of a one-dimensional Brownian motion, respectively. In the present article we generalize this theorem for more general Markov processes as follows: Let $X_t$ be a Markov process and $f(x)$ be a nonnegative, bounded measurable function on the state space. If the expectation of $int^t_0 f(X_s) ds$ is asymptotically equal to a slowly varying function $L(t)$ as $t rightarrow infty$, then, $(1/lambda) int^{L -1(lambda t)}_0 f(X_s) ds$ converges to $ell(M^{-1}(t), 0)$ as $lambda rightarrow infty$, in the sense of the convergence of all finite-dimensional marginal distributions." @default.
- W2069382275 created "2016-06-24" @default.
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- W2069382275 date "1982-08-01" @default.
- W2069382275 modified "2023-09-27" @default.
- W2069382275 title "A Limit Theorem for Slowly Increasing Occupation Times" @default.
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- W2069382275 doi "https://doi.org/10.1214/aop/1176993780" @default.
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