Do you know what the definition of the Itô-integral is, when the limit goes to infinity?
On Wikipedia it says that the fractional brownian motion can be represented as $$B_H(t)=B_H(0)+\frac{1}{\Gamma(H+1/2)}\{\int_{-\infty}^0(t-s)^{H-1/2}-(-s)^{H-1/2}dB(s)\\+\int_0^t(t-s)^{H-1/2}dB(s)\}.$$
They say that it is the Weyl integral. And on the page for the Weyl integral they say that it is a Fourier-series, but I do not quite understand that.
Have you seen infinite Itô-integrals in any books, if so which? Do you know how they are defined?
Usually we define the integral for simple processes. And then we take the limit in probability, can we do something similar when the limit is infinity?