Titre :	Inférence statistique dans les équations différentielles stochastiques
Type de document :	texte imprimé
Auteurs :	Fateh Merahi, Auteur ; Abdelouahab Bibi, Directeur de thèse
Editeur :	جامعة الإخوة منتوري قسنطينة
Année de publication :	2018
Importance :	135 f.
Format :	30 cm.
Note générale :	2 copies imprimées disponibles
Langues :	Français (fre)
Catégories :	Français - Anglais Mathématiques
Tags :	Processus bilinéaire à temps continu  Représentation spectrale  Solution de Itô  Stationnarité  Propriété de longue mémoire  Propriété de Taylor  Processus quadratique  Estimation GMM  Estimations de maximum vraisemblance  Consistance forte  Normalité Asymptotique  Continuous-time bilinear processes  Spectral representation  Itô’s solution  Stationarity  long memory property  Taylor effect  Quadratic processes  (G) MM estimation  YuleWalker estimates  Maximum Likelihood estimates  Strong consistency  Asymptotic Normality  النمط العشوائي ثنائي الخطية بأزمنة مستمرة  تمثيل طيفي  حل إيتو الإستقرار ية  خاصية ذاكرة طويلة  خاصية تايلور  نمط عشوائي تربيعي  مقدر العزوم المعمم  تقدير الإحتمال الأقصى  الكفاءة القوية  التقارب الطبيعي
Index. décimale :	510 Mathématiques
Résumé :	In this thesis, we are studying a class of continuous-time bilinear processes (COBL(1,1)) generated by some stochastic differential equations where we have investigate some probabilistic properties and statistical inference. We use Itô approach for studying the L2 structure of the COBL(1,1) process and its powers for any order with time varying coefficients. Furthermore we prove that these results can be obtained by using the transfer functions approach, moreover, by the spectral representation of the process, we give also conditions for the stability of moments, in particular the moments of the quadratic process provide us to checking the presence of the so called Taylor property for COBL(1,1) process. In a second part of this thesis, we use the results of the first part and we propose some methods of estimation for involving unknown parameters, so, we starting by the moments method (MM) to estimate the parameters by two methods, taking into consideration the relation that exists between the moments of the process and its quadratic version and those associate with the incremented processes where we have showed that the resulting estimators are strongly consistent and asymptotically normal under certain conditions. Using the linear representation of COBL(1,1) process, we are able to propose three other methods, one is in frequency domain and the rest are in time domain and we prove the asymptotic properties of the proposed estimators. Simulation studies are presented in order to illustrate the performances of the different estimators, furthermore, this methods are used to model some real data such as the exchanges rate of the Algerian Dinar against the US-dollar and against the single European currency and the electricity consumption sampled each 15mn in Algeria.
Diplôme :	Doctorat en sciences
En ligne :	../theses/math/MER7232.pdf
Format de la ressource électronique :	pdf
Permalink :	index.php?lvl=notice_display&id=10802

Inférence statistique dans les équations différentielles stochastiques [texte imprimé] / Fateh Merahi, Auteur ; Abdelouahab Bibi, Directeur de thèse . - جامعة الإخوة منتوري قسنطينة, 2018 . - 135 f. ; 30 cm.
2 copies imprimées disponibles

Langues : Français (fre)

Catégories :	Français - Anglais Mathématiques
Tags :	Processus bilinéaire à temps continu  Représentation spectrale  Solution de Itô  Stationnarité  Propriété de longue mémoire  Propriété de Taylor  Processus quadratique  Estimation GMM  Estimations de maximum vraisemblance  Consistance forte  Normalité Asymptotique  Continuous-time bilinear processes  Spectral representation  Itô’s solution  Stationarity  long memory property  Taylor effect  Quadratic processes  (G) MM estimation  YuleWalker estimates  Maximum Likelihood estimates  Strong consistency  Asymptotic Normality  النمط العشوائي ثنائي الخطية بأزمنة مستمرة  تمثيل طيفي  حل إيتو الإستقرار ية  خاصية ذاكرة طويلة  خاصية تايلور  نمط عشوائي تربيعي  مقدر العزوم المعمم  تقدير الإحتمال الأقصى  الكفاءة القوية  التقارب الطبيعي
Index. décimale :	510 Mathématiques
Résumé :	In this thesis, we are studying a class of continuous-time bilinear processes (COBL(1,1)) generated by some stochastic differential equations where we have investigate some probabilistic properties and statistical inference. We use Itô approach for studying the L2 structure of the COBL(1,1) process and its powers for any order with time varying coefficients. Furthermore we prove that these results can be obtained by using the transfer functions approach, moreover, by the spectral representation of the process, we give also conditions for the stability of moments, in particular the moments of the quadratic process provide us to checking the presence of the so called Taylor property for COBL(1,1) process. In a second part of this thesis, we use the results of the first part and we propose some methods of estimation for involving unknown parameters, so, we starting by the moments method (MM) to estimate the parameters by two methods, taking into consideration the relation that exists between the moments of the process and its quadratic version and those associate with the incremented processes where we have showed that the resulting estimators are strongly consistent and asymptotically normal under certain conditions. Using the linear representation of COBL(1,1) process, we are able to propose three other methods, one is in frequency domain and the rest are in time domain and we prove the asymptotic properties of the proposed estimators. Simulation studies are presented in order to illustrate the performances of the different estimators, furthermore, this methods are used to model some real data such as the exchanges rate of the Algerian Dinar against the US-dollar and against the single European currency and the electricity consumption sampled each 15mn in Algeria.
Diplôme :	Doctorat en sciences
En ligne :	../theses/math/MER7232.pdf
Format de la ressource électronique :	pdf
Permalink :	index.php?lvl=notice_display&id=10802