The Annals of Probability

On the Lower Bound of Large Deviation of Random Walks

Tzuu-Shuh Chiang

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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.

Article information

Source
Ann. Probab., Volume 13, Number 1 (1985), 90-96.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993068

Digital Object Identifier
doi:10.1214/aop/1176993068

Mathematical Reviews number (MathSciNet)
MR770630

Zentralblatt MATH identifier
0559.60031

JSTOR
links.jstor.org

Subjects
Primary: 60F10: Large deviations
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Keywords
Random walks

Citation

Chiang, Tzuu-Shuh. On the Lower Bound of Large Deviation of Random Walks. Ann. Probab. 13 (1985), no. 1, 90--96. doi:10.1214/aop/1176993068. https://projecteuclid.org/euclid.aop/1176993068


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