arXiv Analytics

Sign in

arXiv:1705.03584 [math.PR]AbstractReferencesReviewsResources

Lectures on the mean values of functionals -- An elementary introduction to infinite-dimensional probability

Cheng-shi Liu

Published 2017-05-10Version 1

This is an elementary introduction to infinite-dimensional probability. In the lectures, we compute the exact mean values of some functionals on C[0,1] and L[0,1] by considering these functionals as infinite-dimensional random variables. The results show that there exist the complete concentration of measure phenomenon for these mean values since the variances are all zeroes.

Comments: 57
Related articles: Most relevant | Search more
arXiv:1911.07836 [math.PR] (Published 2019-11-18)
A Note on Homogenization of Dynamics and Functionals of Generalized Langevin Systems
arXiv:1802.04224 [math.PR] (Published 2018-02-12)
Large deviations for functionals of Gaussian processes
arXiv:1810.09285 [math.PR] (Published 2018-10-19)
Non-central limit theorems for functionals of random fields on hypersurfaces

Links

Toolbox