Mathematics – Probability
Scientific paper
2008-05-27
Mathematics
Probability
19 pages
Scientific paper
For each $n \geq 1$, let $\{X_{j,n}\}_{1 \leq j \leq n}$ be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process $N_n=\sum_{j=1}^{n}\delta_{X_{j,n}}$ to an infinitely divisible point process. From the point process convergence, we obtain the convergence in distribution of the partial sum sequence $S_n=\sum_{j=1}^{n}X_{j,n}$ to an infinitely divisible random variable, whose L\'{e}vy measure is related to the canonical measure of the limiting point process. As examples, we discuss the case of triangular arrays which possess known (row-wise) dependence structures, like the strong mixing property, the association, or the dependence structure of a stochastic volatility model.
Balan Raluca
Louhichi Sana
No associations
LandOfFree
Convergence of Point Processes with Weakly Dependent Points does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Convergence of Point Processes with Weakly Dependent Points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence of Point Processes with Weakly Dependent Points will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-273840