Simulação exata de processos de difusão não-homogêneos

Abstract

This work addresses the problem of simulating diffusion processes, which are continuous-time stochastic processes widely used in several scientific areas. The processes are defined as the weak solution of stochastic differential equations, which specify the instantaneous mean and variance of the process and are driven by a Brownian motion. The simulation of diffusion processes allows exploring the behavior over time and evaluating the sensitivity to variations in the model parameters. In addition, it is the basis to devise inference algorithms for such processes. The main objective of this dissertation is to study the problem of exact simulation for diffusion processes, in particular, inhomogeneous processes, when the transition distributions of the process are unknown. A modification of the exact algorithm is proposed for this purpose, which reduces its computational cost.