Fast synthesis of persistent fractional Brownian motion

Abstract

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∈ N) values with a small multiple of log₂(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.

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Index Terms

• Computing methodologies

  • Machine learning

    • Machine learning approaches

      • Factorization methods

        • Canonical correlation analysis

  • Modeling and simulation

    • Simulation types and techniques

      • Continuous simulation

• Mathematics of computing

  • Probability and statistics

    • Probabilistic algorithms

    • Probabilistic reasoning algorithms

      • Markov-chain Monte Carlo methods

      • Sequential Monte Carlo methods

    • Statistical paradigms

      • Regression analysis

      • Time series analysis

    • Stochastic processes

• Theory of computation

  • Design and analysis of algorithms