Decomposição da amostra e estimação em difusões ergódicas

Ramos, Luís Decomposição da amostra e estimação em difusões ergódicas. Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa., 2000.

Thesis Type:

Master's Thesis


The required results of stochastic calculus are introduced as well as sufficient conditions for a diffusin to be ergodic. Invariant densities are obtained for two families of diffusion. These families belong the Ornstein-Uhlenbeck and Cox-Ingersoll & Ross diffusions. The moments of transition density of the Cox-Ingersoll & Ross diffusion were obtained and it was shown that this density converges to the invariant density. Lastly a technique, based on sample partition, is given for parameter estimation for ergodic diffusion. A numerical application of that technique for the Ornstein-Uhlenbeck diffusion is given. Final remarks and comments are included.