<html><body><div style="font-family: times new roman, new york, times, serif; font-size: 12pt; color: #000000"><div><br></div><div><span style="FONT-SIZE: medium">Sayın liste üyeleri,</span></div><div style="color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt;" data-mce-style="color: #000; font-weight: normal; font-style: normal; text-decoration: none; font-family: Helvetica,Arial,sans-serif; font-size: 12pt;"><div style="font-family: times new roman, new york, times, serif; font-size: 12pt; color: #000000" data-mce-style="font-family: times new roman, new york, times, serif; font-size: 12pt; color: #000000;"><div style="FONT-SIZE: 12pt; TEXT-DECORATION: none; FONT-FAMILY: Helvetica,Arial,sans-serif; FONT-WEIGHT: normal; COLOR: #000; FONT-STYLE: normal" data-mce-style="font-size: 12pt; text-decoration: none; font-family: Helvetica,Arial,sans-serif; font-weight: normal; color: #000; font-style: normal;"><div style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif; COLOR: #000000" data-mce-style="font-size: 12pt; font-family: times new roman, new york, times, serif; color: #000000;"><div style="FONT-SIZE: 12pt; TEXT-DECORATION: none; FONT-FAMILY: Helvetica,Arial,sans-serif; FONT-WEIGHT: normal; COLOR: #000; FONT-STYLE: normal" data-mce-style="font-size: 12pt; text-decoration: none; font-family: Helvetica,Arial,sans-serif; font-weight: normal; color: #000; font-style: normal;"><div style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif; COLOR: #000000" data-mce-style="font-size: 12pt; font-family: times new roman, new york, times, serif; color: #000000;"><div style="FONT-SIZE: 12pt; TEXT-DECORATION: none; FONT-FAMILY: Helvetica,Arial,sans-serif; FONT-WEIGHT: normal; COLOR: #000; FONT-STYLE: normal" data-mce-style="font-size: 12pt; text-decoration: none; font-family: Helvetica,Arial,sans-serif; font-weight: normal; color: #000; font-style: normal;"><div style="FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif; COLOR: #000000" data-mce-style="font-size: 12pt; font-family: times new roman, new york, times, serif; color: #000000;"><div><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><span style="FONT-SIZE: medium" data-mce-style="font-size: medium;"></span> </p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">İzmir Ekonomi Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü tarafından düzenlenen Matematik – İstatistik Seminerleri </span></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">kapsamında 17 Aralık 2015 perşembe günü Nezihe Turhan tarafından saat 16.00'da M303 no.lu derslikte verilecek seminerin detayları aşağıda belirtilmiştir.</span></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Tüm ilgilenenler davetlidir.</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Saygılarımla,</span></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"> </p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Sevin Gümgüm, PhD</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">İzmir Ekonomi Üniversitesi<br>Matematik Bölümü</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"> </p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">------------------------------------------------------------------------------------------------------------------</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Dear all, İzmir University of Economics, Department of Mathematics continues its Mathematics-Statistics seminars on December 17, 2015, at 16.00pm at M303, with Nezihe Turhan.</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Her talk is entitled as "Limit Theorems for One Class of Ergodic Markov Chains".</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">All are most welcome to attend.</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Please find the more detailed announcement below.</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"> </p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Sincerely</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Sevin Gümgüm, PhD</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"> </p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">İzmir University of Economics</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;">Department of Mathematics</p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"></span> </p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Seminar Details:</span></strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"></span></p><p style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><ul><li style="LINE-HEIGHT: normal" data-mce-style="line-height: normal;"><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Speaker:</span></strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"> Nezihe Turhan<br></span></li><li style="LINE-HEIGHT: normal" data-mce-style="line-height: normal;"><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Title:</span></strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"> Limit Theorems for One Class of Ergodic Markov Chains</span></span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><br></span></li><li style="LINE-HEIGHT: normal" data-mce-style="line-height: normal;"><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Date: </span></strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><span class="Object" id="OBJ_PREFIX_DWT297_com_zimbra_date"><span class="Object" id="OBJ_PREFIX_DWT299_com_zimbra_date">Dec 17</span></span></span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">, 2015</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"> </span></li><li style="LINE-HEIGHT: normal" data-mce-style="line-height: normal;"><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Place: </span></strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">M303</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"> </span></li><li style="LINE-HEIGHT: normal" data-mce-style="line-height: normal;"><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Time: </span></strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">16:00-16:50 </span></li><li style="LINE-HEIGHT: normal" data-mce-style="line-height: normal;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><em><strong><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';">Abstract:</span></strong></em></span></span></span></span><div>We begin with the intuitive background on Markov Chains, and then talk about<br></div><div>the necessity of positive recurrence assumption of a Markov Chain for the existence of<br></div><div>Central Limit Theorem. Then we introduce additive functionals of countable Markov<br></div><div>Chains and talk about two methods, namely, Dˆblin method and Martingale ap-<br>proach, to prove the Central Limit Theorem for the ergodic Loop Markov Chains.<br></div><div>Lastly, we introduce three Loop Markov Chain models, and construct the Central<br></div><div>Limit Theorem for them.</div><p align="left" style="MARGIN: 0px" data-mce-style="margin: 0px;"><br></p><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'" data-mce-style="font-size: 12pt; font-family: 'Times New Roman','serif';"><em><span style="FONT-SIZE: small; FONT-FAMILY: NimbusRomNo9L-Regu" data-mce-style="font-size: small; font-family: NimbusRomNo9L-Regu;"><span style="FONT-SIZE: small; FONT-FAMILY: NimbusRomNo9L-Regu" data-mce-style="font-size: small; font-family: NimbusRomNo9L-Regu;"></span></span></em></span></span></li></ul></div></div></div><div><br></div></div></div><div><br></div></div></div><br></div></div><div><br></div></div></body></html>