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Statistical inference for a stochastic partial differential equation related to an ecological niche
  • Francisco J. Delgado-Vences,
  • Fernando Baltazar-Larios,
  • Liliana Peralta
Francisco J. Delgado-Vences
Conacyt-Instituto de Matematicas UNAM

Corresponding Author:[email protected]

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Fernando Baltazar-Larios
Universidad Nacional Autonoma de Mexico Facultad de Ciencias
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Liliana Peralta
Universidad Nacional Autonoma de Mexico Facultad de Ciencias
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Abstract

In this paper, we use a stochastic partial differential equation (SPDE) as a model for the density of a population under the influence of random external forces/stimuli given by the environment. We 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 SDEs. We prove consistency and asymptotic normality of the estimators; the latter is showed using the Malliavin-Stein method. We illustrate our results with numerical experiments.
Submitted to Mathematical Methods in the Applied Sciences
26 Apr 2024Editorial Decision: Revise Minor
30 Apr 20241st Revision Received
08 May 2024Reviewer(s) Assigned
08 May 2024Review(s) Completed, Editorial Evaluation Pending