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math.PR2009★ 1 cited
On the characteristics of a class of Gaussian processes within the white noise space setting
Daniel Alpay, Haim Attia, David Levanony
Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covarianc…
math.PR2008
Rational functions associated with the white noise space and related topics
Daniel Alpay, David Levanony
Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida's white noise space. The Fueter polynomials are replaced by a basis compute…
math.PR2007
On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions
Daniel Alpay, David Levanony
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with…