Fractional Brownian motion (approximations of fBm): weak and strong approximations and projections

This text studies the relations between fractional Brownian motion and other processes of more simple form.

Financial applications are considered, when we study the financial markets with discrete time and memory and the limit market, constructed in continuous time, is related to fBm.

As an auxiliary but with nteresting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via Wiener process are established and some new inequalities for Gamma-functions, and even for trigonometric functions, are obtained.