12 citations · 16 across the 6 of their papers we have counts for
7 papers
Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes
Daniel Harnett, Arturo Jaramillo, David Nualart
We study the asymptotic behavior of the -symmetric Riemman sums for functionals of a self-similar centered Gaussian process with increment exponent . We prove that, u…
Decomposition and limit theorems for a class of self-similar Gaussian processes
Daniel Harnett, David Nualart
We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A spe…
Central limit theorem for functionals of a generalized self-similar Gaussian process
Daniel Harnett, David Nualart
We consider a class of self-similar, continuous Gaussian processes that do not necessarily have stationary increments. We prove a version of the Breuer-Major theorem for this class…
On Simpson's rule and fractional Brownian motion with H = 1/10
Daniel Harnett, David Nualart
We consider stochastic integration with respect to fractional Brownian motion (fBm) with . The integral is constructed as the limit, where it exists, of a sequence of Riem…
CLT for an iterated integral with respect to fBm with H > 1/2
Daniel Harnett, David Nualart
We construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with res…
Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes
Daniel Harnett, David Nualart
For a Gaussian process and smooth function , we consider a Stratonovich integral of , defined as the weak limit, if it exists, of a sequence of Riemann sums. We give c…
Central limit theorem for a Stratonovich integral with Malliavin calculus
Daniel Harnett, David Nualart
The purpose of this paper is to establish the convergence in law of the sequence of "midpoint" Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian proces…