861 research outputs found
Oscillating Gaussian Processes
In this article we introduce and study oscillating Gaussian processes defined
by , where
are free parameters and is either stationary or
self-similar Gaussian process. We study the basic properties of and we
consider estimation of the model parameters. In particular, we show that the
moment estimators converge in and are, when suitably normalised,
asymptotically normal
A strong convergence to the Rosenblatt process
We give a strong approximation of Rosenblatt process via transport processes
and we give the rate of convergence
Donsker theorem for the Rosenblatt process and a binary market model
International audienceIn this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and simulated data, we show that this approximation performs very well. We use this result to construct a binary market model driven by this process and we show that the model admits arbitrage opportunities
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