New Exponential Probability Inequality and Complete Convergence for F-LNQD Random Variables Sequence With Application to Ar(1)model Generated by F-LNQD Errors

Abstract

The exponential probability inequalities have been important tools in probability and statistics. In this paper, we prove a new tail probability inequality for the distri-butions of sums of conditionally linearly negative quadrant dependent (F-LNQD , in short) random variables, and obtain a result dealing with conditionally complete con-vergence of first-order autoregressive processes with identically distributed (F-LNQD) innovations.

New Tail Probability Type Inequalities and Complete Convergence for Wod Random Variables With Application to Linear Model Generated by Wod Errors

“…Some basic renewal theorems for a random walk with widely dependent increments and gave some applications presented in [3]. The asymptotic of the finite-time ruin probability for a generalized renewal risk model with strong sub exponential claim independent sizes and widely lower orthant dependent inter-occurrence times, studied in [4]. [5] gave the asymptotically equivalent formula for the finite-time ruin probability under a dependent risk model with constant interest rate.…”