<div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr"><br></div><br><br><div dir="ltr"><br><div><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><b><span lang="EN-US" style="font-size:12pt;line-height:115%">Probability Webinar - IM-UFRJ </span></b></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><b><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Dear colleagues,
</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Our next
online seminar will be held on Monday, <b>September
13, </b> from <b>3 p.m. to 4 p.m</b>.
(Rio de Janeiro local time)</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">The Zoom link for the seminar is </span><span lang="EN-US"></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><a href="https://us02web.zoom.us/j/83698166702?pwd=ejFxYmh3dVk5b3J3SG0wMWxEVnVrUT09" style="color:blue" target="_blank"><span lang="EN-US" style="font-family:Arial,sans-serif;color:rgb(17,85,204);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">https://us02web.zoom.us/j/83698166702?pwd=ejFxYmh3dVk5b3J3SG0wMWxEVnVrUT09</span></a><span lang="EN-US"></span></p><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><br></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-size:12pt;line-height:115%">Speaker: </span><b>Alexandre de
Bustamante Simas (UFPB & Kaust)</b><b><span style="font-size:12pt;line-height:115%"></span></b></p>
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<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Title:
</span><b><span lang="EN-US">Approximations of the covariance operators of
solutions of fractional elliptic SPDEs driven by Gaussian white noise</span></b><span lang="EN-US"></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Abstract:
</span><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span><span lang="EN-US" style="font-size:12pt;line-height:115%;color:black"> </span><span lang="EN-US" style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">In this talk we will briefly present the model we are
interested in, which is a fractional elliptic stochastic partial differential
equation driven by Gaussian white noise. There is in the literature a standard
way to approximate the covariance operator of the solution of such equations,
the so-called rational approximation (Bolin and Kirchner, 2020), however this
approach uses the solution to build such an approximation. By considering
directly the covariance operator, we are able to provide a more
computationally efficient approximation. We compute the rate of
this approximation in terms of the Hilbert-Schmidt norm. Furthermore, we
also obtain, rigorously, the rate of approximation of the so-called lumped
mass method. This method is widely used by practitioners and is essential
to make it computationally feasible to fit some models in spatial statistics.
We obtain the rate of approximation of the lumped mass method in terms of the
operator's norm as well as, under some additional restrictions, the
Hilbert-Schmidt norm. Finally, we present the usage of these approximations in
maximum likelihood estimation. Joint
work with David Bolin and Zhen Xiong.</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%;color:black"> </span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">All the talks
are held in English. </span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">The videos of
the online seminars are available:</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">2020 - <a href="http://www.dme.ufrj.br/?page_id=2885" target="_blank">http://www.dme.ufrj.br/?page_id=2885</a></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">2021-1 -
<a href="http://www.dme.ufrj.br/?page_id=3027" target="_blank">http://www.dme.ufrj.br/?page_id=3027</a></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">For the second semester, a few days after each meeting
the video should be available at <a href="http://www.dme.ufrj.br/?page_id=3178" target="_blank">http://www.dme.ufrj.br/?page_id=3178</a></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Thanks for circulating this information. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Sincerely, <br>
Organizers: Guilherme Ost and Maria Eulalia Vares</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span></p></div></div><div id="m_-3436058078872376017DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br> <table style="border-top:1px solid #d3d4de">
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