most recent 30 from http://mathoverflow.net 2013-05-21T07:42:28Z http://mathoverflow.net/feeds/question/25637 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/25637/follmer-calcul-dito-sans-probabilites-in-english-or-german vonjd 2010-05-23T08:33:41Z 2012-01-20T10:43:58Z

<p>Does anybody know a translation of <a href="http://archive.numdam.org/ARCHIVE/SPS/SPS_1981__15_/SPS_1981__15__143_0/SPS_1981__15__143_0.pdf" rel="nofollow">Föllmer: Calcul d'Ito sans probabilités</a> in English or German?</p> <p>It seems to be a very interesting text - Abstract: "It is shown that if a deterministic continuous curve has a 'quadratic variation' in a suitable sense (which however depends explicitly on a nested sequence of time subdivisions, for example the standard dyadic one), then it satisfies a deterministic 'Ito formula' when composed with a twice differentiable function. Thus the only place where probability really appears in the derivation of Ito's formula is in the fact that, given any sequence of subdivisions, almost every path of a semimartingale admits a quadratic variation relative to this sequence (though no path may exist which has a quadratic variation relative to all sequences)"</p> <p>See also: <a href="http://mathoverflow.net/questions/16664/convergence-and-non-convergence-of-left-point-and-mid-point-riemann-sums" rel="nofollow">http://mathoverflow.net/questions/16664/convergence-and-non-convergence-of-left-point-and-mid-point-riemann-sums</a> and first answer.</p> <p>Other references along the same lines would also be appreciated - Thank you!</p>

http://mathoverflow.net/questions/25637/follmer-calcul-dito-sans-probabilites-in-english-or-german/25706#25706 Andrey Rekalo 2010-05-23T18:41:18Z 2010-05-23T18:41:18Z

<p>Föllmer's approach was mainly adopted by specialists in Mathematical Finance. </p> <p>Have a look at <a href="http://books.google.co.uk/books?id=KKLa1j-diXwC&amp;printsec=frontcover&amp;dq=Introduction+to+Stochastic+Calculus+for+Finance%3A+A+New+Didactic+Approach&amp;source=bl&amp;ots=-L3eKT8OjQ&amp;sig=3Md3B6gg4LLy2Uzzzy8fs37Rwqo&amp;hl=en&amp;ei=4HT5S6P-OI6Q4gbxh9AI&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=5&amp;ved=0CC8Q6AEwBA#v=onepage&amp;q&amp;f=false" rel="nofollow"><em>Introduction to Stochastic Calculus for Finance</em></a> by D. Sondermann. This is an intro lecture course based on the work of Föllmer. And the book contains an English translation of the original article by Föllmer in the Appendix.</p>

http://mathoverflow.net/questions/25637/follmer-calcul-dito-sans-probabilites-in-english-or-german/26672#26672 The Bridge 2010-06-01T05:48:19Z 2010-06-01T05:48:19Z

<p>By the way I forgot to mention Rough Path Theory There is a book by Victoir and Fritz which seems to be quite complete account on the subject and that treats Itô stochastic Integration Theory </p> <p>Regards</p>

http://mathoverflow.net/questions/25637/follmer-calcul-dito-sans-probabilites-in-english-or-german/86194#86194 GdReis 2012-01-20T10:43:58Z 2012-01-20T10:43:58Z

<p>By the way, there is a recent preprint in arXiv (<a href="http://arxiv.org/abs/1108.2981" rel="nofollow">Nutz2010.Pathwise construction of stochastic integrals</a>) where the author develops a general construction for Stochastic integrals without probability. The construction includes the integrals that can be constructed via Follmer's approach.</p>