## Electronic Journal of Probability

### Large Deviations for Processes in Random Environments with Jumps

Ivan Matic

#### Abstract

A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We study the exponential decay of the probabilities that the walk will reach sites located far away from the origin. We also study a similar problem for the continuous analogue: the process that is a solution to an ODE with random coefficients. In this second model the environment also has teleports'' which are the regions from where the process can make discontinuous jumps.

#### Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 87, 2406-2438.

Dates
Accepted: 23 November 2011
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464820256

Digital Object Identifier
doi:10.1214/EJP.v16-962

Mathematical Reviews number (MathSciNet)
MR2861679

Zentralblatt MATH identifier
1244.60028

Subjects
Primary: 60F10: Large deviations
Secondary: 60G10: Stationary processes

Rights

#### Citation

Matic, Ivan. Large Deviations for Processes in Random Environments with Jumps. Electron. J. Probab. 16 (2011), paper no. 87, 2406--2438. doi:10.1214/EJP.v16-962. https://projecteuclid.org/euclid.ejp/1464820256

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