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dc.contributor.authorMerahi, Fateh
dc.contributor.authorBibi, Abdelouahab
dc.date.accessioned2018-05-10T11:50:12Z
dc.date.available2018-05-10T11:50:12Z
dc.date.issued2018-04-26
dc.identifier.urihttp://hdl.handle.net/123456789/136323
dc.description.abstractIn 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.fr_FR
dc.language.isofrfr_FR
dc.publisherجامعة الإخوة منتوري قسنطينةfr_FR
dc.subjectProcessus bilinéaire à temps continufr_FR
dc.subjectReprésentation spectralefr_FR
dc.subjectSolution de Itôfr_FR
dc.subjectStationnaritéfr_FR
dc.subjectPropriété de longue mémoirefr_FR
dc.subjectPropriété de Taylorfr_FR
dc.subjectProcessus quadratiquefr_FR
dc.subjectEstimation GMMfr_FR
dc.subjectEstimations de maximum vraisemblancefr_FR
dc.subjectConsistance fortefr_FR
dc.subjectNormalité Asymptotiquefr_FR
dc.subjectالنمط العشوائي ثنائي الخطية بأزمنة مستمرةfr_FR
dc.subjectحل إيتوfr_FR
dc.subjectالإستقرار يةfr_FR
dc.subjectخاصية ذاكرة طويلةfr_FR
dc.subjectخاصية تايلورfr_FR
dc.subjectنمط عشوائي تربيعيfr_FR
dc.subjectمقدر العزوم المعممfr_FR
dc.subjectتقدير الإحتمال الأقصىfr_FR
dc.subjectالكفاءة القويةfr_FR
dc.subjectالتقارب الطبيعيfr_FR
dc.subjectتمثيل طيفيfr_FR
dc.titleInférence statistique dans les équations différentielles stochastiquesfr_FR
dc.typeThesisfr_FR


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