English

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

R2 v1 2026-06-22T11:42:53.410Z