<div dir="ltr"><br><div class="gmail_quote"><div dir="ltr"><br><div class="gmail_quote"><br><div dir="ltr">



















<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><b><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> Probability Webinar  -- IM-UFRJ  - 24/08</span></span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><br></span></p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Dear colleagues,<span> 
</span><span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Our next online seminar will be held next Monday,
August 24, from <b>3 p.m. to 4 p.m</b>. (Rio de Janeiro local time)<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">The GoogleMeet link for the seminars is: </span><a href="https://meet.google.com/nxh-optr-wtq" style="color:blue;text-decoration:underline" target="_blank"><span style="font-size:12pt;line-height:115%" lang="EN-US">https://meet.google.com/nxh-optr-wtq</span></a><span style="font-size:12pt;line-height:115%" lang="EN-US"> 
<br>
<br>
<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Speaker: <span> </span>Daniel<span> 
</span>Yasumasa Takahashi<span>  </span>(UFRN) </span><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif"" lang="EN-US"><span></span></span></p>

<table cellpadding="0" border="0">
 <tbody><tr>
  <td style="padding:0cm"><br></td>
 </tr>
</tbody></table>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Title:</span><span style="font-size:12pt;line-height:115%" lang="EN-US"> </span><b><span style="font-size:12pt;line-height:115%" lang="EN-US">Mixing rates for processes
with long-memory</span></b><span style="font-size:12pt;line-height:115%" lang="EN-US"><span></span></span></p>

<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Abstract:<b> </b></span><span style="font-size:12pt;line-height:115%" lang="EN-US"> Non-Markovian
processes are ubiquitous, but they are much less understood compared to Markov
processes.  </span><span style="font-size:12pt;line-height:115%">We
model non-Markovianity using probability kernels that can depend on its entire
history. The continuity rate characterizes how the dependence of kernel on the
past decays. One key question is to understand how the mixing rates and decay
of correlation are related to the continuity rate. Pollicot (2000) and
Bressaud, Fernandez, Galves (1999) showed that if the continuity rate decays as
O(1/n^c), for c > 1, then the correlation also decays as O(1/n^c).
Johansson, Oberg, Pollicott (2007) proved the uniqueness of the stationary
measure compatible with kernels with the continuity rate in O(1/n^c), for c
> 1/2. Moreover, Berger, Hoffman, Sidoravicius (2018) established that there
are kennels with multiple compatible measures whenever c < 1/2. Therefore,
the natural question is to understand the mixing rates and correlation decays
when c is in [1/2,1]. In this talk, I will exhibit upper bounds for the mixing
rates and correlation decays when the continuity rate decays as  O(1/n^c),
for c in (1/2,1].  If time allows, I will show how to apply the result to
prove a new weak invariance principle. This talk is based on joint work with
Christophe Gallesco.<span></span></span></p>

<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> </span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><br></span></p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">All the talks are held in English. <span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Thanks for circulating this information. <span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Sincerely, <br>
<br>
<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Organizers: Guilherme Ost and
Maria Eulalia Vares<span></span></span></p>





</div>
</div></div>
</div></div>