Analysis of the Rosenblatt process

By Ciprian A. Tudor. 2006

228 citations recorded by the source corpus.

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Major (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Ito multiple integral with respect to the Brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin calculus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/72e77f8bdd4165c83e46ff29a76a1a5cf06ae04a

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Citations in the corpus

Generalized Hermite processes, discrete chaos and limit theorems (2013, methodology): “Recent works include Tudor [30], Bardet and Tudor [2], Veillette and Taqqu [32], Maejima and Tudor [15, 16].”
Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes (2008, methodology): “[14] I. Nourdin, D. Nualart and C.A. Tudor (2007): Central and non-central limit theorems for weighted ower variations of fractional Brownian motion.”
Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, methodology): “We refer the reader to [30] and [32] for further details on the Rosenblatt process.”
Neutral stochastic partial differential equations with delay driven by Rosenblatt process in a Hilbert space (2015, unknown): “1 (Tudor, 2008).”
Variations and estimators for selfsimilarity parameters via Malliavin calculus (2009, unknown): “The Rosenblatt process can be represented as follows (see [29]): for every t ∈ [0,1], Z(t) := Z(t) = d(H) ∫ t 0 ∫ t 0 [ ∫ t y1∨y2 ∂1K H′(u, y1) (3.”
Variations and Hurst index estimation for a Rosenblatt process using longer filters (2009, methodology): “[27] C.A. Tudor (2008): Analysis of the Rosenblatt process.”
Properties and numerical evaluation of the Rosenblatt distribution (2013, background): “Various integral representations can be found in [32].”
On the distribution of the Rosenblatt process (2013, background): “(See Pipiras and Taqqu (2010), Tudor (2008), Tudor and Viens (2009), Veillette and Taqqu (in press) among others.)”