Estimação em processos advindos da solução da equação de Langevin

• Main Author: Pinto, Douglas Rodrigues
• Other Authors: Lopes, Silvia Regina Costa
• Format: Others
• Language: Portuguese
• Published: 2016
• Subjects: Estimacao de parametros; Equação de Langevin
• Online Access: http://hdl.handle.net/10183/140885

This paper presents the results of the estimations made in the process arising from the solution of classical Langevin equation with Brownian motion noise, and generalized, with α-stable noise. We perform the estimation of the parameter λ related to the memory function of such processes and the parameter α when the noise is a process with α-stable distribution. The estimation of λ is obtained from the maximum likelihood method, the ordinary least squares method and from the sample autocovariance function of the process. We discuss the types of noise that may be associated to the Langevin equation and present the Existence and Uniqueness theorem of Kannan and Kannan representation formula, which prove the existence and uniqueness of the solution for the generalized Langevin equation and presents criteria for the form of such solution.