Central Limit Theorem for Linear Stochastic Evolutions

• Autores: Makoto Nakashima
• Localización: Journal of mathematics of Kyoto University, ISSN 0023-608X, Vol. 49, Nº 1, 2009, págs. 201-224
• Idioma: inglés
• DOI: 10.1215/kjm/1248983037
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• Resumen

  • 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.