Inference for a Stochastic Partial Differential Equations related to an ecological niche.
In this talk, we use a stochastic partial differential equation (SPDE) as a model for the density of a population. Indeed, we are interested in modeling animal density under the influence of random external forces/stimuli given by the environment. We want to study statistical properties for two crucial parameters of the SPDE that describe the dynamic of the system. To do that we use the Galerkin projection to transform the problem, passing from the SPDE to a system of independent SDEs; in this manner, we are able to find the Maximum likelihood estimator of the parameters. We validate the method by using simulations of the SPDE. We show consistency and asymptotic normality of the estimators; the latter is proved using the Malliavin-Stein method. These will allow us to fit the model to actual data.
Area: CS22 - Statistics for Stochastic Processes and applications (Chiara Amorino)
Keywords: SPDEs; statistical inference; simulations; Galerkin approximation
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