<div dir="ltr"><span style="font-size:12.8px">Ito only holds if </span><img alt="f \in C^{1,2}" title="f \in C^{1,2}" class="gmail-m_-8807083006366393510va_li gmail-CToWUd gmail-hoverZoomLink hoverZoomLink" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09f%09%5Cin%09C%5E%7B1,2%7D" id="gmail-m_-8807083006366393510l0.9626291348556639" height="17" width="58" style="font-size: 12.8px; display: inline; vertical-align: -3.3px;"><span style="font-size:12.8px"> -- I don't know of any examples where the conditions fail, but the formula still holds. For the formula to make sense even, (but not satisfy the conditions) you would need for the derivatives to exist, but not be continuous, so it's not that simple to even try and look for examples where it might hold with less regularity on f. </span><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Nov 15, 2017 at 11:28 AM, Lucas Duarte Bahia <span dir="ltr"><<a href="mailto:lduarteb@andrew.cmu.edu" target="_blank">lduarteb@andrew.cmu.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">In the notes we have:<div><br></div><div><img src="cid:ii_15fc0805556d9449" alt="Inline image 2" width="494" height="126"></div><div><br></div><div>Is C1,2 a necessary and sufficient condition, or just a sufficient condition?</div><div><br></div><div>What I mean is if f is not C1,2 is there any case where I can still apply Itô?<br><div><br clear="all"><div><div class="m_-9040343135886316145gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><p style="font-size:12.8px">Thanks,</p><div style="font-size:12.8px"><b>Lucas Duarte Bahia</b></div><div style="font-size:12.8px">MS. Computational Finance Student</div><div style="font-size:12.8px">Carnegie Mellon University</div><div style="font-size:12.8px">Telephone: <a href="tel:(412)%20378-1892" value="+14123781892" style="color:rgb(17,85,204)" target="_blank">(412) 378-1892</a></div></div></div></div>
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