During eighteenth and early nineteenth centuries it was widely believed that every continuous function has a well defined tangent - at least at ``almost all'' points. As the Weierstrass function shows that this is clearly not the case. The function is named after Karl Weierstrass who presented it in a lecture for the Berlin Academy in 1872 [1].

Alternative examples of continuous and nowhere differentiable functions are given by the sample paths of standard Brownian motion, also known as the Wiener process or white noise. It was to handle such ill behaved processes, which have important applications to both pure and applied mathematics, that the techniques of stochastic calculus were developed.