Modélisation stochastique et estimation de la dispersion du pollen de maïs.
Estimation dans des modèles à volatilité stochastique.

Abstract : The first part of this work is devoted to the study of corn pollen dispersion. The pollen grain is seen as a particle subjected to a field of forces and its path is modelled using diffusion processes. In an homogeneous case (two contiguous corn fields), different parametric individual dispersal functions are obtained using different assumptions for stopping time of stochastic processes. From the experiments the parameters are estimated using a non-linear regression model. The choice of the most fitted model is then obtained using a criterion of Akaïke type and graphic methods. Moreover these models allow to make predictions. The results are then applied when two fields are separated by another culture (heterogeneous case), in order to study the effect of a discontinuity on dispersion.
In the second part, we study mean-reverting stochastic volatility models, often used in economy. The observed process is related to a non observable diffusion for which there are unknown parameters to estimate. First a two steps statistical method is proposed based on the ARMA(1,1) structure of the process, by using a moment estimator and a Whittle contrast. Simulations are made in order to compare this method with some known methods. Second a leverage parameter is introduced and a discretized model is studied. An auxiliary criterion is proposed to estimate the parameters using an indirect inference method. Finally simulations are made to evaluate their performances.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00011584
Contributor : Agnès Grimaud <>
Submitted on : Friday, February 10, 2006 - 3:08:04 PM
Last modification on : Sunday, March 31, 2019 - 1:19:26 AM
Long-term archiving on : Saturday, April 3, 2010 - 10:20:50 PM

Identifiers

  • HAL Id : tel-00011584, version 1

Citation

Agnès Grimaud. Modélisation stochastique et estimation de la dispersion du pollen de maïs.
Estimation dans des modèles à volatilité stochastique.. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2005. Français. ⟨tel-00011584⟩

Share

Metrics

Record views

3964

Files downloads

1908