Inférence statistique dans les équations différentielles stochastiques

الموضوعات

إحصاء

روابط وملفات

التعريف والنوع

رقم الوثيقة

fdc8d31d-7676-4538-b032-01274d1f74dd

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

790849_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":" Abdelouahab Bibi","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Fateh Merahi","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

French

المصدر والدورية

اسم المصدر

Inférence statistique dans les équations différentielles stochastiques

المحتوى والصفحات

عدد الصفحات

0

ترجمة الملخص

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 probabilisticproperties and statistical inference. We use Itô approach for studying the L2 structure of theCOBL(1,1) process and its powers for any order with time varying coefficients. Furthermore weprove that these results can be obtained by using the transfer functions approach, moreover, bythe 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 socalled Taylor property for COBL(1,1) process. In a second part of this thesis, we use the resultsof 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 itsquadratic version and those associate with the incremented processes where we have showedthat the resulting estimators are strongly consistent and asymptotically normal under certainconditions. Using the linear representation of COBL(1,1) process, we are able to propose threeother methods, one is in frequency domain and the rest are in time domain and we prove theasymptotic properties of the proposed estimators. Simulation studies are presented in order toillustrate the performances of the different estimators, furthermore, this methods are used tomodel some real data such as the exchanges rate of the Algerian Dinar against the US-dollarand against the single European currency and the electricity consumption sampled each 15mnin Algeria.

إشراف وإعداد

الإشراف

Abdelouahab Bibi

الإعداد

Fateh Merahi

الاقتباسات الببليوغرافية