LIMIT THEOREMS FOR RANDOM TRIANGULAR URN SCHEMES

Journal Article

Rafik, Aguech . 2009

• نوع عمل المنشور: Research paper
• رابط المنشور على الويب: PDF file
• الوسوم: Paper
• المجلة \ الصحيفة: Journal of Applied Probability
• رقم العدد: 3
• رقم الإصدار السنوي: 46
• الصفحات: 827 إلى 843

مستخلص المنشور

In this paper we study a generalized Pólya urn with balls of two colors and a random triangular replacement matrix. We extend some results of Janson (2004), (2005) to the case where the largest eigenvalue of the mean of the replacement matrix is not in the dominant class. Using some useful martingales and the embedding method introduced in Athreya and Karlin (1968), we describe the asymptotic composition of the urn after the nth draw, for large n.