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Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes | | Daniel Harnett
; Arturo Jaramillo
; David Nualart
; | | Date: |
13 Jun 2017 | | Abstract: | We study the asymptotic behavior of the $
u$-symmetric Riemman sums for
functionals of a self-similar centered Gaussian process $X$ with increment
exponent $0<alpha<1$. We prove that, under mild assumptions on the covariance
of $X$, the law of the weak $
u$-symmetric Riemman sums converge in the
Skorohod topology when $alpha=(2ell+1)^{-1}$, where $ell$ denotes the
smallest positive integer satisfying $int_{0}^{1}x^{2j}
u(dx)=(2j+1)^{-1}$
for all $j=0,dots, ell-1$. In the case $alpha>(2ell+1)^{-1}$, we prove that
the convergence holds in probability. | | Source: | arXiv, 1706.3890 | | Services: | Forum | Review | PDF | Favorites | |
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