Fast Synthesis of Persistent Fractional Brownian Motion

Due to the relevance of self-similarity analysis in several research areas, there is an increased interest in methods to generate realizations of self-similar processes, namely in the ones capable of simulating long-range dependence. This article describes a new algorithm to approximate persistent fractional Brownian motions with a predefined Hurst parameter. The algorithm presents a computational complexity of O(n) and generates sequences with n (n is an element of N) values with a small multiple of log(2)(n) variables. Because it operates in a sequential manner, the algorithm is suitable for simulations demanding real-time operation. A network traffic simulator is presented as one of its possible applications.