MULTIFRACTIONAL PROCESSES WITH RANDOM EXPONENT

By Antoine Ayache, Murad S. Taqqu. 2005

115 citations recorded by the source corpus.

Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Holder regularity and their self-similarity.

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Citations in the corpus

Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates (2017, background): “However, some more general functions were introduced for H, for example with singularities, like the generalized multifractional Brownian motion [3], or even as a stochastic process [4].”
Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics (2020, background): “Extensions of the fBm include some specificities for the Hurst exponent: it may vary deterministically through time, as in the multifractional Brownian motion [63, 8, 16, 28], it may be a random process, as in the multifractional process with random exponent [4, 11, 27, 29], or it may even be asymme”
Stochastic properties of the linear multifractional stable motion (2004, methodology): “Since these two seminal works appeared, many authors have studied other finite-variance, locally self-similar models that extend the MBM process (see, for example, Ayache and Lévy-Véhel (2000) and Ayache and Taqqu (2003)).”
Wavelet construction of Generalized Multifractional processes. (2007, methodology): “Throughout this article, the complex-valued Brownian measure dW is chosen in a way that all the processes and the fields we consider are real-valued (see for example [6] or [8]).”
MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “We end this paragraph by noting that the use of a fractional Brownian field permits further generalizations: for instance, a multifractional process with random exponent is defined in [6], and a self-regulating process is considered in [30].”
Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity (2013, methodology): “…zHere, H-sssi is the self-similar of parameter H with stationary increments (see Samorodnitsky and Taqqu 1994 for a detailed discussion). xIndeed, Ayache and Taqqu (2005) provide sufficient conditions for a multifractional process with a random functional parameter to be self-similar (in the…”