Access the full text.
Sign up today, get DeepDyve free for 14 days.
We study the asymptotic behavior of the $$\nu $$ ν -symmetric Riemann sums for functionals of a self-similar centered Gaussian process X with increment exponent $$0<\alpha <1$$ 0 < α < 1 . We prove that, under mild assumptions on the covariance of X, the law of the weak $$\nu $$ ν -symmetric Riemann sums converge in the Skorohod topology when $$\alpha =(2\ell +1)^{-1}$$ α = ( 2 ℓ + 1 ) - 1 , where $$\ell $$ ℓ denotes the largest positive integer satisfying $$\int _{0}^{1}x^{2j}\nu (\mathrm{d}x)=(2j+1)^{-1}$$ ∫ 0 1 x 2 j ν ( d x ) = ( 2 j + 1 ) - 1 for all $$j=0,\dots , \ell -1$$ j = 0 , ⋯ , ℓ - 1 . In the case $$\alpha >(2\ell +1)^{-1}$$ α > ( 2 ℓ + 1 ) - 1 , we prove that the convergence holds in probability.
Journal of Theoretical Probability – Springer Journals
Published: May 30, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.