An estimation of distribution algorithm for the computation of innovation estimators of diffusion processes
This work addresses the problem of initial value sensitivity in Innovation Estimators for diffusion processes, offering a global optimization alternative for researchers in stochastic modeling.
The paper proposes using an Estimation of Distribution Algorithm (UMDAc) to compute Innovation Estimators for diffusion processes, showing substantial improvement in estimator effectiveness for complex nonlinear and stochastic dynamics.
Estimation of Distribution Algorithms (EDAs) and Innovation Method are recognized methods for solving global optimization problems and for the estimation of parameters in diffusion processes, respectively. Well known is also that the quality of the Innovation Estimator strongly depends on an adequate selection of the initial value for the parameters when a local optimization algorithm is used in its computation. Alternatively, in this paper, we study the feasibility of a specific EDA - a continuous version of the Univariate Marginal Distribution Algorithm (UMDAc) - for the computation of the Innovation Estimators. Numerical experiments are performed for two different models with a high level of complexity. The numerical simulations show that the considered global optimization algorithms substantially improves the effectiveness of the Innovation Estimators for different types of diffusion processes with complex nonlinear and stochastic dynamics.