Series representations of fractional Gaussian processes by trigonometric and Haar systems.
Hausdorff dimension of the graph of the fractional Brownian sheet.
Construction of non separable dyadic compactly supported orthonormal wavelet bases for L(R) of arbitrarily high regularity.
By means of simple computations, we construct new classes of non separable QMF's. Some of these QMF's will lead to non separable dyadic compactly supported orthonormal wavelet bases for L(R) of arbitrarily high regularity.
Joint continuity of the local times of fractional brownian sheets
Let ={ (), ∈ℝ } be an (, )-fractional brownian sheet with index =( , …, )∈(0, 1) defined by ()=( (), …, ()) (∈ℝ ), where , …, are independent copies of a real-valued fractional brownian sheet . We prove that if <∑ ...
Multifractional processes with random exponent.
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 Hölder regularity and their self-similarity.
Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times
By using a wavelet method we prove that the harmonisable-type -parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (, )-mfBm and to obtain some new results concerning its sample path behavior.
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