Abstract
In this note, we prove for a large class of random walks on $R^n$ that $\lim \inf_{n\rightarrow\infty}(1/n)\log P_x(L_n(\omega, \cdot) \in N) \geq - I(\mu)$ where $L_n(\omega, \cdot)$ is the occupation measure, $N$ is a weak neighborhood of $\mu$ and $I(\mu)$ is the usual Donsker-Varadhan functional. This generalizes a previous theorem of the author where the state space is assumed to be compact.
Citation
Tzuu-Shuh Chiang. "On the Lower Bound of Large Deviation of Random Walks." Ann. Probab. 13 (1) 90 - 96, February, 1985. https://doi.org/10.1214/aop/1176993068
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