Expected Regularized Total Variation of Brownian Motion
Probability
2015-11-12 v1
Abstract
We introduce a notion of regularized total variation on an interval for continuous functions with unbounded variation. The definition of regularized total variation is obtained from that of total variation by subtracting a penalty for the size of the partition used to estimate the variation. We present an explicit construction of a partition achieving the regularized total variation, and use this construction to estimate the expected regularized total variation of Brownian motion on an interval.
Keywords
Cite
@article{arxiv.1511.03633,
title = {Expected Regularized Total Variation of Brownian Motion},
author = {Alexander Dunlap},
journal= {arXiv preprint arXiv:1511.03633},
year = {2015}
}
Comments
11 pages, 1 figure