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In [BP10b] studieren sie asymptotische Eigenschaften des Maximum-Likelihood-Schätzers für α. Obiges Korollar ergibt sich im Falle x=y=0 auch aus dem Beweis von Lemma 3 in [BP10b]. Die folgende Proposition ist eine Verallgemeinerung von [BP10b, Theorem 21], wo der Fall x=y=0 behandelt wird. Folgende Proposition folgt im Falle x=y=0 aus [BP10b, Theorem 20].
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Parameter estimation problem for models of SDE with time-dependent drift have been considered by many authors (for instance see Mishra and Prakasa Rao 1985; Liptser and Shiryaev 2001 and recently, Barczy and Pap 2010; Höpfner and Kutoyants 2010; Dehling et al. 2010).
In a recent paper Barczy and Pap (2010) have investigated the MLE for a time-inhomogeneous diffusion process given by the SDE ...
Then the central limit theorem for integrales with respect to Brownian motion (see e.g. Feigin 1976; see also Kutoyants 2004, Theorem 1.19; Barczy and Pap 2010) entails the convergence in law ...
As we do not prove the convergence of J_T/T^2 in probability, the results in (Barczy and Pap 2010) cannot be applied here to establish Theorem 3.
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For a comprehensive study, two kinds of outliers are considered: Additive outliers (AO) and Innovative outliers (IO). The definitions of AO and IO (Barczy et al. 2010) are provided below. (A Khoo, Ong, Biswas cikkben nem szerepel ugyan explicit módon az irodalomjegyzékben az "Innovational Outliers in INAR(1) Models" cikk, de ezen cikk arXiv verziójára törtenik hivatkozás, ezért adtuk meg ezt az idezőt.)
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<div class="Citation short-list"> <div class="publication Publication">Forrásközlemény: [1347272] Mátyás Barczy et al. α-Wiener Bridges: Singularity of Induced Measures and Sample Path Properties. (2010) STOCHASTIC ANALYSIS AND APPLICATIONS 0736-2994 1532-9356 28 3 447-466 </div> <div class="related Publication" style="margin-top: 6px; margin-left: 20px">Idéző: <div class="JournalArticle Publication short-list"> <div class="authors"> <span class="author-name" > Hildebrandt, Florian ✉ </span> <span class="author-type"> </span> ; <span class="author-name" > Roelly, Sylvie </span> <span class="author-type"> </span> </div ><div class="title"><a href="/gui2/?mode=browse¶ms=publication;30960009" mtid="30960009" target="_blank">Pinned Diffusions and Markov Bridges</a></div> <div class="pub-info"> <span class="journal-title">JOURNAL OF THEORETICAL PROBABILITY</span> <span class="journal-volume">33</span> : <span class="journal-issue">2</span> <span class="page"> pp. 906-917. , 12 p. </span> <span class="year">(2020)</span> </div> <div class="pub-end"><div class="identifier-list"> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="10.1007/s10959-019-00954-5" target="_blank" href="https://doi.org/10.1007%2Fs10959-019-00954-5"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="000494214600001" target="_blank" href="http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=CustomerName&SrcApp=CustomerName&DestLinkType=FullRecord&KeyUT=000494214600001&DestApp=WOS"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="85074470613" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074470613"> Scopus </a> </span> </span> </div> <span class="short-pub-prop-list"> <span class="short-pub-mtid"> Közlemény:30960009 </span> <span class="status-holder"><span class="status-data status-ADMIN_APPROVED"> Admin láttamozott </span></span> <span class="pub-core"> Idéző Duplumgyanú </span> <span class="pub-type">Folyóiratcikk (Szakcikk ) </span> <!-- && !record.category.scientific --> <span class="pub-category">Tudományos</span> </span> </div> </div> </div> <div class="citation" style="margin-top: 6px; margin-left: 20px"><i>Kapcsolat: [28486913] <span class="status-data status-VALIDATED"> Egyeztetett </span> | <span class="externalCitation-data externalCitation-true"> Független </span> | Magyarországi szerző: Nem vizsgált | Külföldi kiadás: Igen | Eredete: WoS-XML | Említések száma: 1 </i></div> <ol> </ol> </div>
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<div class="Citation short-list"> <div class="publication Publication">Forrásközlemény: [1347272] Mátyás Barczy et al. α-Wiener Bridges: Singularity of Induced Measures and Sample Path Properties. (2010) STOCHASTIC ANALYSIS AND APPLICATIONS 0736-2994 1532-9356 28 3 447-466 </div> <div class="related Publication" style="margin-top: 6px; margin-left: 20px">Idéző: <div class="JournalArticle Publication short-list"> <div class="authors"> <span class="author-name" > Kuang, Nenghui ✉ </span> <span class="author-type"> </span> ; <span class="author-name" > Liu, Bingquan </span> <span class="author-type"> </span> </div ><div class="title"><a href="/gui2/?mode=browse¶ms=publication;30960011" mtid="30960011" target="_blank">Least squares estimator for alpha-sub-fractional bridges</a></div> <div class="pub-info"> <span class="journal-title">STATISTICAL PAPERS</span> <span class="journal-volume">59</span> : <span class="journal-issue">3</span> <span class="page"> pp. 893-912. , 20 p. </span> <span class="year">(2018)</span> </div> <div class="pub-end"><div class="identifier-list"> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1007/s00362-016-0795-2" target="_blank" href="https://doi.org/10.1007%2Fs00362-016-0795-2"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000441916300003" target="_blank" href="http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=CustomerName&SrcApp=CustomerName&DestLinkType=FullRecord&KeyUT=000441916300003&DestApp=WOS"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="84978100416" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84978100416"> Scopus </a> </span> </span> </div> <span class="short-pub-prop-list"> <span class="short-pub-mtid"> Közlemény:30960011 </span> <span class="status-holder"><span class="status-data status-VALIDATED"> Egyeztetett </span></span> <span class="pub-core"> Idéző</span> <span class="pub-type">Folyóiratcikk (Szakcikk ) </span> <!-- && !record.category.scientific --> <span class="pub-category">Tudományos</span> </span> </div> </div> </div> <div class="citation" style="margin-top: 6px; margin-left: 20px"><i>Kapcsolat: [28486915] <span class="status-data status-VALIDATED"> Egyeztetett </span> | <span class="externalCitation-data externalCitation-true"> Független </span> | Magyarországi szerző: Nem vizsgált | Külföldi kiadás: Igen | Eredete: WoS-XML | Említések száma: 1 </i></div> <ol> <li> [Hivatkozás adatai:605397] </li> </ol> </div>
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Neben [Man04] spielen die folgenden Artikel für die vorliegende Arbeit eine Rolle: Barczy und Pap beschäftigen sich in [BP10a] mit Pfadeigenschaften und zeigen die paarweise Singularität der Verteilungen von (1) für verschiedene Werte von α. Für den Fall x=y=0 wird die Verteilung in [BP10a, Lemma 2.1] bestimmt. Ein Beweis ist schließlich in [BP10a, Lemma 3.1] zu finden. Wir werden nun einen alternativen Beweis für (36) präsentieren. Unser Beweis basiert auf der in [Øks03, Aufgabe 5.11] für die Brownsche Brücke vorgeschlagenen Vorgehensweise. Anschließend stellen wir auch den Beweis aus [BP10a] vor und vergleichen schließlich die beiden Beweismethoden. Wir präsentieren nun den in [BP10a] geführten Beweis für (36).
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