On the characteristics of a class of Gaussian processes within the white noise space setting

By Daniel Alpay, H. Attia, David Levanony. 2009

33 citations recorded by the source corpus.

Using the white noise space framework, we construct and study a class of Gaussian processes with stationary increments, which include as particular cases the Brownian and fractional Brownian motions. The derivative processes are computed using Hida's theory of stochastic distributions.

Subfields: Economics and Econometrics, Finance

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Citations in the corpus

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, background): “Proof: the first identity in (2) follows from H(a)1 = 0, and the second one from bii(a) + bjj(a)− 2bij(a) = cij − 1 2cii − 1 2cjj , itself a consequence of the form (1) bij(a) = −12cij + γi + γj for some vector γ.”
Stochastic Processes Induced by Singular Operators (2011, unknown): “D. Alpay, H. Attia, and D. Levanony (2010).”
On Free Stochastic Processes and their Derivatives (2013, unknown): “The key is is to estimate integrals of the form (1) The previous result, together with the existence of a V˚age type inequality in G − 1 , allows to deﬁne stochastic integrals as in Theorem 7.6. g (2) Finally we remark that the analysis in the papers [2, 3]”
A class of Gaussian processes with fractional spectral measures (2010, background): “One common point between the previous work [3] and the present work is the construction of an operator Qσ from a subspace of L2(R, dx) into 31”