<div dir="ltr"><p class="gmail-MsoTitle" style="text-align:center"><span style="font-size:18pt;font-family:"times new roman",serif"><b>SEMINARIO
DI MATEMATICA</b><span></span></span></p>

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<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif">Mercoledì 26 ottobre 2016</span><span style="font-size:16pt;font-family:"times new roman",serif"><span></span></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif">ore 14:30<span></span></span></p>

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<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><u><span style="font-size:16pt;font-family:"times new roman",serif">Scuola Normale Superiore<span></span></span></u></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif">Pisa<span></span></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Aula Bianchi<span></span></span></p>

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<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span style="font-size:22pt;font-family:"times new roman",serif">Arnaud Debussche<span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="font-size:9.5pt;font-family:arial,sans-serif">(</span><i><span style="font-family:"times new roman",serif">Rennes University)</span></i><span style="font-size:9.5pt;font-family:arial,sans-serif"><span></span></span></p>

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<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:"times new roman",serif">terrà un
seminario dal titolo:<span></span></span></p>

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<pre style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:20pt;font-family:"times new roman",serif;color:black">“</span></b><b><span lang="EN-US" style="font-size:20pt;font-family:"times new roman",serif">A new regularity result for the Kolmogorov </span></b></pre><pre style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:20pt;font-family:"times new roman",serif">equation for SPDEs with multiplicative noise</span></b><b><span lang="EN-US" style="font-size:20pt;font-family:"times new roman",serif;color:black">”</span></b><b><span lang="EN-US" style="font-size:20pt;font-family:"times new roman",serif"><span></span></span></b></pre>

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<p class="MsoNormal" style="text-align:justify"><b><span lang="EN-US" style="font-family:"times new roman",serif">Abstract:<span></span></span></b></p>

<pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">In this talk we present a new regularity result on the solution of the Kolmogorov equation <span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">associated to a stochastic parabolic PDE of the type: <span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">$$<span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">du=(\partial_{xx} u + f(u))dt + \sigma(u) dW<span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">$$<span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">with boundary conditions and initial data. We prove a new estimate on the second differential of the solution <span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">of this Kolmogorov equation. This is crucial for the study of the weak order of numerical scheme and we<span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">apply this to a time discretization of the equation.<span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">The main tool is a formula for the second differential which is obtained thanks to Malliavin calculus.<span></span></span></i></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">This is a joint work with C.E. Bréhier.<span></span></span></i></pre>

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<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif">Tutti gli interessati sono invitati a
partecipare.<span></span></span></p>

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<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif">Classe di Scienze Matematiche e Naturali<span></span></span></p><p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><br></span></p><p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><br></span></p><p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><br></span></p><div><div class="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div>
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