Abstract
We provide a large probability bound on the uniform approximation of fractional Brownian motion with Hurst parameter H, by a deep-feedforward ReLU neural network fed with a N-dimensional Gaussian vector, with bounds on the network design (number of hidden layers and total number of neurons). Essentially, up to log terms, achieving an uniform error of O(N−H) is possible with log(N) hidden layers and O(NlogN) parameters. Our analysis relies, in the standard Brownian motion case (H=1/2), on the Levy construction and in the general fractional Brownian motion case (H≠1/2), on the Lemarié-Meyer wavelet representation. This work gives theoretical support on new generative models based on neural networks for simulating continuous-time processes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.