## Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 7, Number 2 (1997), 362-381.

### Functional large deviation principles for first-passage-time processes

Anatolii A. Puhalskii and Ward Whitt

#### Abstract

We apply an extended contraction principle and superexponential convergence in probability to show that a functional large deviation principle for a sequence of stochastic processes implies a corresponding functional large deviation principle for an associated sequence of first-passage-time or inverse processes. Large deviation principles are established for both inverse processes and centered inverse processes, based on corresponding results for the original process. We apply these results to obtain functional large deviation principles for renewal processes and superpositions of independent renewal processes.

#### Article information

**Source**

Ann. Appl. Probab., Volume 7, Number 2 (1997), 362-381.

**Dates**

First available in Project Euclid: 14 October 2002

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1034625336

**Digital Object Identifier**

doi:10.1214/aoap/1034625336

**Mathematical Reviews number (MathSciNet)**

MR1442318

**Zentralblatt MATH identifier**

0885.60023

**Subjects**

Primary: 60F10: Large deviations

Secondary: 60G55: Point processes 60K05: Renewal theory

**Keywords**

Large deviations large deviation principle Skorohod topologies contraction principle first passage times inverse processes counting processes renewal processes superpositions of renewal processes

#### Citation

Puhalskii, Anatolii A.; Whitt, Ward. Functional large deviation principles for first-passage-time processes. Ann. Appl. Probab. 7 (1997), no. 2, 362--381. doi:10.1214/aoap/1034625336. https://projecteuclid.org/euclid.aoap/1034625336