## Journal of Applied Probability

- J. Appl. Probab.
- Volume 48, Number 3 (2011), 688-698.

### Sample path large deviations of Poisson shot noise with heavy-tailed semiexponential distributions

Ken R. Duffy and Giovanni Luca Torrisi

#### Abstract

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

#### Article information

**Source**

J. Appl. Probab., Volume 48, Number 3 (2011), 688-698.

**Dates**

First available in Project Euclid: 23 September 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1316796907

**Digital Object Identifier**

doi:10.1239/jap/1316796907

**Mathematical Reviews number (MathSciNet)**

MR2884808

**Zentralblatt MATH identifier**

1230.60025

**Subjects**

Primary: 60F10: Large deviations

**Keywords**

Heavy-tailed distribution sample path large deviation Poisson shot noise

#### Citation

Duffy, Ken R.; Torrisi, Giovanni Luca. Sample path large deviations of Poisson shot noise with heavy-tailed semiexponential distributions. J. Appl. Probab. 48 (2011), no. 3, 688--698. doi:10.1239/jap/1316796907. https://projecteuclid.org/euclid.jap/1316796907