OpenGrey (Institut de l'Information Scientifique et Technique) · 1995 · 334 citations · 0 references
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EngineeringMathematicsMultiscale ModelingProbability TheoryStochastic ProcessesBrownian MotionContinuous-time Stochastic ProcessesDiffusion ProcessesMonte Carlo MethodsPoint ProcessesStochastic CalculusBrownian Motion AnalysisFractional Brownian MotionHausdorff DistanceMultifractal Processes
We generalize the definition of the fractional Brownian motion of exponent H to the case where H is no longer a constant, but a function of the time index of the process. This allows us to model non stationary continuous processes, and we show that H(t) and 2 \\Gamma H(t) are indeed respectively the local Holder exponent and the local box and Hausdorff dimension at point t. Finally, we propose a simulation method and an estimation procedure for H(t) for our model.