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    <p class="MsoTitle"><span
        style="font-size:18.0pt;font-family:"Times New
        Roman","serif"">SEMINARIO
        <span style="mso-no-proof:yes">MATEMATICA</span><o:p></o:p></span></p>
    <p class="MsoTitle"><span
        style="font-size:10.0pt;font-family:"Times New
        Roman","serif""><o:p><span
            style="text-decoration:none"> </span></o:p></span></p>
    <p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
      line-height:18.0pt;tab-stops:324.0pt" align="center"><span
        style="font-size:16.0pt;font-family:
        "Times New Roman","serif";mso-no-proof:yes">Martedì
        11 marzo 2014</span><span
        style="font-size:16.0pt;font-family:"Times New
        Roman","serif""><o:p></o:p></span></p>
    <p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
      line-height:18.0pt;tab-stops:324.0pt" align="center"><span
        style="font-size:16.0pt;font-family:
        "Times New Roman","serif"">ore <span
          style="mso-no-proof:yes">15:00</span><o:p></o:p></span></p>
    <p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
      line-height:18.0pt;tab-stops:324.0pt" align="center"><span
        style="font-size:16.0pt;font-family:
        "Times New Roman","serif""><o:p> </o:p></span></p>
    <p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
      line-height:18.0pt;tab-stops:324.0pt" align="center"><u><span
          style="font-size:16.0pt;
          font-family:"Times New Roman","serif"">Scuola
          Normale Superiore<o:p></o:p></span></u></p>
    <p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
      line-height:18.0pt;tab-stops:324.0pt" align="center"><span
        style="font-size:16.0pt;font-family:
        "Times New Roman","serif"">Pisa<o:p></o:p></span></p>
    <p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
      line-height:18.0pt;tab-stops:324.0pt" align="center"><span
        style="font-size:16.0pt;font-family:
        "Times New Roman","serif"">Aula <span
          style="mso-no-proof:yes">Mancini</span><o:p></o:p></span></p>
    <p class="MsoNormal" style="tab-stops:324.0pt"><b><u><span
            style="font-size:10.0pt;
            font-family:"Times New Roman","serif""><o:p><span
                style="text-decoration:none"> </span></o:p></span></u></b></p>
    <p class="MsoNormal" style="tab-stops:324.0pt"><b><u><span
            style="font-size:10.0pt;
            font-family:"Times New Roman","serif""><o:p><span
                style="text-decoration:none"> </span></o:p></span></u></b></p>
    <pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><span style="font-size:24.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">Michael Roeckner<o:p></o:p></span></b></pre>
    <p class="MsoNormal" style="text-align:center;mso-layout-grid-align:
      none;text-autospace:none" align="center"><i
        style="mso-bidi-font-style:normal"><span
          style="font-family:"Times New
          Roman","serif";mso-ansi-language:EN-US"
          lang="EN-US">(University
          of Bielefeld)<o:p></o:p></span></i></p>
    <p class="MsoNormal" style="text-align:center" align="center"><i
        style="mso-bidi-font-style:
        normal"><span style="font-family:"Times New
          Roman","serif";
          mso-ansi-language:EN-US" lang="EN-US">joint work with Viorel
          Barbu (Romanian Academy, Iasi)<o:p></o:p></span></i></p>
    <p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
      align="center"><span
        style="font-size:16.0pt;font-family:"Times New
        Roman","serif""><o:p> </o:p></span></p>
    <p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
      align="center"><span
        style="font-size:16.0pt;font-family:"Times New
        Roman","serif"">Terrà un
        seminario dal titolo:<o:p></o:p></span></p>
    <p class="MsoNormal" style="tab-stops:324.0pt"><b
        style="mso-bidi-font-weight:
        normal"><span style="font-family:"Times New
          Roman","serif""><o:p> </o:p></span></b></p>
    <p class="MsoNormal" style="text-align:center;mso-layout-grid-align:
      none;text-autospace:none" align="center"><b
        style="mso-bidi-font-weight:normal"><i
          style="mso-bidi-font-style:normal"><span
            style="font-size:22.0pt;
            font-family:"Times New
            Roman","serif";mso-ansi-language:EN-US"
            lang="EN-US">“</span></i></b><b
        style="mso-bidi-font-weight:normal"><span
          style="font-size:22.0pt;
          font-family:"Times New
          Roman","serif";mso-ansi-language:EN-US"
          lang="EN-US">An operatorial
          approach to stochastic<o:p></o:p></span></b></p>
    <p class="MsoNormal" style="text-align:center;mso-layout-grid-align:
      none;text-autospace:none" align="center"><b
        style="mso-bidi-font-weight:normal"><span
          style="font-size:22.0pt;font-family:"Times New
          Roman","serif";
          mso-ansi-language:EN-US" lang="EN-US">partial differential
          equations driven by<o:p></o:p></span></b></p>
    <p class="MsoNormal" style="text-align:center;mso-layout-grid-align:
      none;text-autospace:none" align="center"><b
        style="mso-bidi-font-weight:normal"><span
          style="font-size:22.0pt;font-family:"Times New
          Roman","serif"">linear
          multiplicative noise</span></b><b
        style="mso-bidi-font-weight:normal"><i
          style="mso-bidi-font-style:normal"><span
            style="font-size:22.0pt;
            font-family:"Times New
            Roman","serif";mso-ansi-language:EN-US"
            lang="EN-US">”</span></i></b><b
        style="mso-bidi-font-weight:normal"><span
          style="font-size:22.0pt;font-family:
          "Times New Roman","serif""><o:p></o:p></span></b></p>
    <p class="MsoNormal" style="text-align:center" align="center"><b
        style="mso-bidi-font-weight:
        normal"><span style="font-family:"Times New
          Roman","serif";
          mso-ansi-language:EN-US" lang="EN-US"><o:p> </o:p></span></b></p>
    <p class="MsoNormal" style="text-align:justify"><b
        style="mso-bidi-font-weight:
        normal"><span style="font-family:"Times New
          Roman","serif";
          mso-ansi-language:EN-US" lang="EN-US">Abstract:<o:p></o:p></span></b></p>
    <p class="MsoNormal"
      style="text-align:justify;line-height:9.0pt;mso-line-height-rule:
exactly;mso-layout-grid-align:none;punctuation-wrap:simple;text-autospace:none;
      mso-line-break-override:restrictions"><span
        style="font-family:"Times New
        Roman","serif";
mso-fareast-font-family:PMingLiU;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">In<span style="letter-spacing:-.45pt"> </span>this<span
          style="letter-spacing:-.4pt"> </span><span
          style="letter-spacing:-.05pt">talk,</span><span
          style="letter-spacing:-.3pt"> </span><span
          style="letter-spacing:-.2pt">we</span><span
          style="letter-spacing:-.45pt"> </span><span
          style="letter-spacing:-.1pt">develop</span><span
          style="letter-spacing:-.4pt"> </span>a<span
          style="letter-spacing:-.4pt"> </span>new<span
          style="letter-spacing:-.4pt"> </span>general<span
          style="letter-spacing:-.4pt"> </span><span
          style="letter-spacing:-.05pt">approach</span><span
          style="letter-spacing:-.4pt"> </span>to<span
          style="letter-spacing:-.4pt"> </span>the<span
          style="letter-spacing:-.4pt"> </span><span
          style="letter-spacing:-.1pt">exis</span><span
          style="letter-spacing:-.05pt">tence</span><span
          style="letter-spacing:-.4pt"> </span>and<span
          style="letter-spacing:-.45pt"> </span>unique-ness<span
          style="letter-spacing:
          1.15pt"> </span>theory<span style="letter-spacing:1.15pt"> </span>of<span
          style="letter-spacing:1.15pt"> </span>infinite<span
          style="letter-spacing:1.15pt">
        </span>dimensional<span style="letter-spacing:1.15pt"> </span><span
          style="letter-spacing:-.05pt">sto</span><span
          style="letter-spacing:-.1pt">c</span><span
          style="letter-spacing:-.05pt">hastic</span><span
          style="letter-spacing:1.2pt"> </span>equations<span
          style="letter-spacing:1.2pt"> </span>of<span
          style="letter-spacing:1.15pt"> </span>the<span
          style="letter-spacing:1.15pt"> </span>form<span
          style="letter-spacing:1.15pt"> </span><span
          style="letter-spacing:.15pt;mso-bidi-font-style:italic">dX</span><span
          style="letter-spacing:.1pt">(<span
            style="mso-bidi-font-style:italic">t</span>)</span><span
          style="letter-spacing:-.25pt"> </span>+</span><span
        style="font-family:"Times New
        Roman","serif";mso-font-width:115%;mso-ansi-language:
        EN-US;mso-bidi-font-style:italic" lang="EN-US">A</span><span
        style="font-family:
        "Times New
Roman","serif";mso-fareast-font-family:PMingLiU;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">(<span style="mso-bidi-font-style:italic">t,<span
            style="letter-spacing:-1.7pt"> </span><span
            style="letter-spacing:.05pt">X</span></span><span
          style="letter-spacing:.05pt">(<span
            style="mso-bidi-font-style:italic">t</span>))</span><span
          style="letter-spacing:.1pt;mso-bidi-font-style:italic">dt</span><span
          style="letter-spacing:-.7pt;mso-bidi-font-style:italic"> </span>=<span
          style="letter-spacing:-.4pt"> </span><span
          style="letter-spacing:.05pt;
          mso-bidi-font-style:italic">X</span><span
          style="letter-spacing:.05pt">(<span
            style="mso-bidi-font-style:italic">t</span>)</span><span
          style="letter-spacing:
          .1pt;mso-bidi-font-style:italic">dW</span><span
          style="letter-spacing:-1.95pt;
          mso-bidi-font-style:italic"> </span>(<span
          style="mso-bidi-font-style:italic">t</span>)<span
          style="letter-spacing:-.35pt"> </span>in<span
          style="letter-spacing:-.35pt"> </span>(0<span
          style="mso-bidi-font-style:italic">,<span
            style="letter-spacing:-1.7pt"> </span>T<span
            style="letter-spacing:-1.9pt"> </span></span>)<span
          style="letter-spacing:-1.85pt">
        </span></span><span style="font-family:"Times New
        Roman","serif";
mso-fareast-font-family:Meiryo;mso-font-width:115%;mso-ansi-language:EN-US;
        mso-bidi-font-style:italic" lang="EN-US">×<span
          style="letter-spacing:-2.75pt"> </span><span
          style="letter-spacing:.4pt">H</span></span><span
        style="font-family:
        "Times New
Roman","serif";mso-fareast-font-family:PMingLiU;letter-spacing:.35pt;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">,</span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:PMingLiU;
letter-spacing:-.25pt;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US"> </span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
PMingLiU;letter-spacing:-.1pt;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">whe</span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
PMingLiU;letter-spacing:-.05pt;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">re</span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
PMingLiU;letter-spacing:-.35pt;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US"> </span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
PMingLiU;mso-font-width:115%;mso-ansi-language:EN-US;mso-bidi-font-style:italic"
        lang="EN-US">A<span style="letter-spacing:-.55pt"> </span></span><span
        style="font-family:
        "Times New
Roman","serif";mso-fareast-font-family:PMingLiU;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">is<span style="letter-spacing:-.35pt"> </span>a<span
          style="letter-spacing:-.35pt"> </span><span
          style="letter-spacing:-.05pt">time-dependent</span><span
          style="letter-spacing:-.35pt"> </span>nonlinear</span><span
        style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:PMingLiU;
letter-spacing:2.1pt;mso-font-width:113%;mso-ansi-language:EN-US"
        lang="EN-US"> </span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
        PMingLiU;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">monotone<span style="letter-spacing:-.2pt"> </span>and<span
          style="letter-spacing:-.15pt"> </span><span
          style="letter-spacing:-.1pt">demicon</span><span
          style="letter-spacing:-.05pt">tin</span><span
          style="letter-spacing:-.1pt">uous</span><span
          style="letter-spacing:-.2pt"> </span>operator<span
          style="letter-spacing:-.15pt"> </span>from<span
          style="letter-spacing:-.2pt"> </span><span
          style="mso-bidi-font-style:italic">V<span
            style="letter-spacing:1.45pt"> </span></span>to<span
          style="letter-spacing:-.15pt"> </span><span
          style="mso-bidi-font-style:italic">V<span
            style="letter-spacing:-1.4pt"> </span><span
            style="position:relative;
            top:-3.5pt;mso-text-raise:3.5pt;letter-spacing:.25pt">I</span></span><span
          style="letter-spacing:.2pt">,</span><span
          style="letter-spacing:-.15pt"> </span><span
          style="letter-spacing:-.1pt">coercive</span><span
          style="letter-spacing:-.15pt">
        </span>and<span style="letter-spacing:-.2pt"> </span>with<span
          style="letter-spacing:-.15pt"> </span>p<span
          style="letter-spacing:.05pt">oly-</span></span><span
        style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
        PMingLiU;mso-font-width:110%;mso-ansi-language:EN-US"
        lang="EN-US">nomial<span style="letter-spacing:1.25pt"> </span><span
          style="letter-spacing:-.05pt">growth.</span><span
          style="letter-spacing:.75pt"> </span>Here,<span
          style="letter-spacing:1.45pt"> </span><span
          style="mso-bidi-font-style:italic">V<span
            style="letter-spacing:.45pt"> </span></span>is<span
          style="letter-spacing:1.25pt"> </span>a<span
          style="letter-spacing:1.25pt"> </span><span
          style="letter-spacing:-.1pt">reflexive</span><span
          style="letter-spacing:1.3pt">
        </span><span style="letter-spacing:-.05pt">Banach</span><span
          style="letter-spacing:
          1.3pt"> </span>space<span style="letter-spacing:1.25pt"> </span><span
          style="letter-spacing:-.1pt">c</span><span
          style="letter-spacing:-.05pt">ontinuously</span><span
          style="letter-spacing:1.2pt"> </span>and<span
          style="letter-spacing:1.3pt"> </span>densely<span
          style="letter-spacing:1.45pt"> </span><span
          style="letter-spacing:-.05pt">embedded</span><span
          style="letter-spacing:.55pt"> </span>in<span
          style="letter-spacing:.55pt"> </span>a<span
          style="letter-spacing:.55pt"> </span>Hilbert<span
          style="letter-spacing:.55pt">
        </span>space<span style="letter-spacing:.6pt"> </span><span
          style="mso-bidi-font-style:
          italic">H<span style="letter-spacing:1.25pt"> </span></span>of<span
          style="letter-spacing:.55pt"> </span>(generalized)<span
          style="letter-spacing:
          .5pt"> </span><span style="letter-spacing:-.05pt">functions</span><span
          style="letter-spacing:.55pt"> </span>on<span
          style="letter-spacing:.6pt"> </span>a<span
          style="letter-spacing:.55pt"> </span>domain<span
          style="letter-spacing:.55pt"> </span></span><span
        style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
Meiryo;mso-font-width:110%;mso-ansi-language:EN-US;mso-bidi-font-style:italic"
        lang="EN-US">O<span style="letter-spacing:-.45pt"> </span></span><span
        style="font-family:
        "Cambria
        Math","serif";mso-fareast-font-family:Meiryo;mso-bidi-font-family:
"Cambria
Math";mso-font-width:110%;mso-ansi-language:EN-US;mso-bidi-font-style:
        italic" lang="EN-US">⊂</span><span
        style="font-family:"Times New
        Roman","serif";
mso-fareast-font-family:Meiryo;letter-spacing:-.8pt;mso-font-width:110%;
        mso-ansi-language:EN-US;mso-bidi-font-style:italic" lang="EN-US">
      </span><span style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:Meiryo;
        mso-font-width:110%;mso-ansi-language:EN-US" lang="EN-US">R<span
          style="position:relative;
          top:-3.5pt;mso-text-raise:3.5pt;mso-bidi-font-style:italic">d</span></span><span
        style="font-family:"Times New
        Roman","serif";mso-fareast-font-family:
        PMingLiU;mso-ansi-language:EN-US" lang="EN-US"><span
          style="mso-spacerun:yes"> </span><span
          style="mso-font-width:110%">and<span
            style="letter-spacing:.05pt"> </span><span
            style="mso-bidi-font-style:italic">V<span
              style="letter-spacing:-.45pt"> </span><span
              style="position:relative;top:-3.5pt;mso-text-raise:3.5pt">I<span
                style="letter-spacing:1.1pt"> </span></span></span>is<span
            style="letter-spacing:
            .05pt"> </span>the<span style="letter-spacing:.1pt"> </span>dual<span
            style="letter-spacing:.05pt"> </span>of<span
            style="letter-spacing:.1pt"> </span><span
            style="mso-bidi-font-style:italic">V<span
              style="letter-spacing:2.5pt"> </span></span>in<span
            style="letter-spacing:.05pt"> </span>the<span
            style="letter-spacing:.1pt"> </span><span
            style="letter-spacing:-.05pt">duality</span><span
            style="letter-spacing:.05pt">
          </span>induced<span style="letter-spacing:.1pt"> </span><span
            style="letter-spacing:
            -.15pt">by</span><span style="letter-spacing:.05pt"> </span><span
            style="mso-bidi-font-style:italic">H<span
              style="letter-spacing:.8pt"> </span></span>as<span
            style="letter-spacing:.05pt"> </span><span
            style="letter-spacing:-.1pt">pivot</span><span
            style="letter-spacing:.1pt"> </span>space.<span
            style="letter-spacing:2.1pt"> </span><span
            style="letter-spacing:-.1pt">Furthermore,</span></span> </span><span
        style="font-family:"Times New
        Roman","serif";mso-font-width:115%;
        mso-ansi-language:EN-US;mso-bidi-font-style:italic" lang="EN-US">W<span
          style="letter-spacing:
          1.1pt"> </span></span><span style="font-family:"Times
        New Roman","serif";
mso-fareast-font-family:PMingLiU;mso-font-width:115%;mso-ansi-language:EN-US"
        lang="EN-US">is<span style="letter-spacing:.05pt"> </span>a<span
          style="letter-spacing:.1pt"> </span>Wiener<span
          style="letter-spacing:.1pt"> </span>process<span
          style="letter-spacing:.1pt"> </span>in<span
          style="letter-spacing:.1pt"> </span><span
          style="letter-spacing:.4pt;
          mso-bidi-font-style:italic">H</span><span
          style="letter-spacing:.35pt">.</span><span
          style="letter-spacing:1.35pt"> </span>The<span
          style="letter-spacing:.1pt"> </span>new<span
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    <pre class="moz-signature" cols="72">-- 
--------------------------------------------------------------------------------
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
Tel. 050-509260
Piazza dei Cavalieri, 7
56126 Pisa
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</a>
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:classi@sns.it">classi@sns.it</a>
 
Le informazioni contenute nella presente e-mail e nei relativi allegati possono essere riservate e sono, comunque, destinate esclusivamente al destinatario in indirizzo.
E’ vietata, pertanto, la diffusione, distribuzione e/o copiatura di tali informazioni da parte di qualsiasi soggetto diverso dal destinatario.
Chiunque abbia ricevuto o letto questa e-mail per errore o senza esserne legittimato è invitato a darne immediatamente notizia  al mittente tramite fax o e-mail e a distruggerla.
Grazie.
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