Self-similar processes are stochastic processes that are invariant in distribution under
suitable time scaling, and are a subject intensively studied in the last few decades. This …

We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the
Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a …

On the distribution of the Rosenblatt process - ScienceDirect Skip to main contentSkip to article
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Fix ν> 0, denote by G (ν/2) a Gamma random variable with parameter ν/2 and let n≥ 2 be a
fixed even integer. Consider a sequence {F k} k≥ 1 of square integrable random variables …

Let Z denote a Hermite process of order q≥ 1 and self-similarity parameter H∈(1 2, 1). This
process is H-self-similar, has stationary increments and exhibits long-range dependence …

We study a least square-type estimator for an unknown parameter in the drift coefficient of a
stochastic differential equation with additive fractional noise of Hurst parameter H> 1/2 H> …

Let q≧2 be a positive integer, B be a fractional Brownian motion with Hurst index H∈, Z be
an Hermite random variable of index q, and H_q denote the q th Hermite polynomial. For …

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of
two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt …

The generalized Rosenblatt process is obtained by replacing the single critical exponent
characterizing the Rosenblatt process by two different exponents living in the interior of a …

This is an overview of some recent techniques involving the Malliavin calculus of variations
and the so-called 'Stein's method'for the Gaussian approximations of probability …