## Journal of Mathematics of Kyoto University

- J. Math. Kyoto Univ.
- Volume 49, Number 1 (2009), 201-224.

### Central Limit Theorem for Linear Stochastic Evolutions

#### Abstract

We consider a Markov chain with values in [0,$\infty$)$^{\mathbb{z}d}$. The Markov chain includes some interesting examples such as the oriented site percolation, the directed polymers in random environment, and a time discretization of the binary contact process. We prove a central limit theorem for “the spatial distribution of population” when $d\geq 3$ and a certain square-integrability condition for the total population is satisfied. This extends a result known for the directed polymers in random environment to a large class of models.

#### Article information

**Source**

J. Math. Kyoto Univ., Volume 49, Number 1 (2009), 201-224.

**Dates**

First available in Project Euclid: 30 July 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.kjm/1248983037

**Digital Object Identifier**

doi:10.1215/kjm/1248983037

**Mathematical Reviews number (MathSciNet)**

MR2531137

**Zentralblatt MATH identifier**

1171.60005

#### Citation

Nakashima, Makoto. Central Limit Theorem for Linear Stochastic Evolutions. J. Math. Kyoto Univ. 49 (2009), no. 1, 201--224. doi:10.1215/kjm/1248983037. https://projecteuclid.org/euclid.kjm/1248983037