## The Annals of Probability

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

### On the Lower Bound of Large Deviation of Random Walks

#### 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