In [[Föllmer 81]](http://archive.numdam.org/ARCHIVE/SPS/SPS_1981__15_/SPS_1981__15__143_0/SPS_1981__15__143_0.pdf) (English translation to be found [here](http://books.google.co.uk/books?id=KKLa1j-diXwC&printsec=frontcover&dq=Introduction+to+Stochastic+Calculus+for+Finance%3A+A+New+Didactic+Approach&source=bl&ots=-L3eKT8OjQ&sig=3Md3B6gg4LLy2Uzzzy8fs37Rwqo&hl=en&ei=4HT5S6P-OI6Q4gbxh9AI&sa=X&oi=book_result&ct=result&resnum=5&ved=0CC8Q6AEwBA#v=onepage&q&f=false)) writes: "The class of processes of quadratic variation is clearly larger than the class of semimartingales: Just consider a deterministic process of quadratic variation which is of unbounded variation."


Could anyone please give me examples (with references) of *deterministic processes of quadratic variation which are of unbounded variation*? Thank you!


(P.S.: What seems to make these deterministic processes interesting is that you also have to use [Ito integrals](http://en.wikipedia.org/wiki/Ito_calculus) to integrate them)



Examples of deterministic processes of quadratic variation which are of unbounded variation
Take $f:[0,1]\to\mathbb{R}$ such that $f(0)=0$ and it interpolates linearly between $f(1/n)=\frac{(-1)^n}{n}$ for any natural $n$. 


