2008/05/13 by Lisandro Fermín, Lisandro J. Fermin, Fermin, Lisandro J.
Economics, Econometrics and Finance · Environmental Science · Mathematics · #60F05 #60F15 #60G10 #Analysis of environmental and stochastic processes #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.PR #math.ST #msc:60F05 #msc:60F15 #msc:60G10 #stat.TH
paper · pdf · doi:10.48550/arxiv.0805.1949
33 pages
arxiv created 2008/05/13 · openalex publication_date 2008/05/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to extend the aggregation convergence results given in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle and Fermin 2008) to doubly stochastic linear and nonlinear processes with weakly dependent innovations. First, we introduce a weak dependence notion for doubly stochastic processes, based in the weak dependence definition given in (Doukhan and Louhichi 1999), and we exhibe several models satisfying this notion, such as: doubly stochastic Volterra processes and doubly stochastic Bernoulli scheme with weakly dependent innovations. Afterwards we derive a central limit theorem for the partial aggregation sequence considering weakly dependent doubly stochastic processes. Finally, show a new SLLN for the covariance function of the partial aggregation process in the case of doubly stochastic Volterra processes with interactive innovations. Keywords: Aggregation, weak dependence, doubly stochastic processes, Volterra processes, Bernoulli shift, TCL, SLLN.