Some Nonparametric Asymptotic Results for a Class of Stochastic Processes

This paper provides a solution of a generalized eigenvalue problem for integrated processes of order 2 in a nonparametric framework. Our analysis focuses on a pair of random matrices related to such integrated process. The matrices are constructed considering some weight functions. Under asymptotic conditions on such weights, convergence results in distribution are obtained and the generalized eigenvalue problem is solved. Differential equations and stochastic calculus theory are used. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Statistics - Theory and Methodson 13 July 2010 , available online: http://www.tandfonline.com/10.1080/03610920903061021