# Student Probability Seminar

#### Weighted Sums of Regularly Varying Random Variables with Dependent Weights

Speaker: Moumanti Podder

Location: Warren Weaver Hall 905

Date: Tuesday, November 19, 2013, 3:30 p.m.

Synopsis:

Our work aims to study the tail behaviour of weighted sums of the form $$\sum_{t=1}^\infty X_t\prod_{j=1}^t Y_j$$ ,where both the sequences $$\{X_t\}$$ and $$\{Y_t\}$$ are independent and identically distributed, with each $$X_t$$ having a regularly varying tail, and $$(X_t,Y_t)$$ jointly following the bivariate Sarmanov distribution. With assumptions similar to those used by Denisov and Zwart (2007) imposed on these two sequences, and with certain suitably summable bounds similar to those proposed by Hazra and Maulik (2012), we try to explore the tail distribution of the random variables $$\sup_{k\leq n} \sum_{t=1}^k X_t \prod Y_j$$ and $$\sup \sum_{t=1}^n X_t \prod Y_j$$.