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Fast synthesis of persistent fractional Brownian motion

Fast Synthesis of Persistent Fractional Brownian Motion PEDRO R. M. INACIO, MARIO M. FREIRE, and MANUELA PEREIRA, Instituto de Telecomunicacoes and University of Beira Interior ˜ PAULO P. MONTEIRO, Nokia Siemens Networks Portugal S. A. and Instituto de Telecomunicacoes ˜ 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 longrange dependence. This article describes a new algorithm to approximate persistent fractional Brownian motions with a prede ned Hurst parameter. The algorithm presents a computational complexity of O(n) and generates sequences with n (n ˆ 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 traf c simulator is presented as one of its possible applications. Categories and Subject Descriptors: F.2.0 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems ”General; G.3 [Mathematics of Computing]: Probability and Statistics ” Correlation and regression analysis; probabilistic algorithms (including Monte Carlo); stochastic processes; time series analysis; I.6.8 [Simulation and Modeling]: Types of Simulation ”Continuous; Monte Carlo General Terms: Algorithms, Performance, Theory, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

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