English

Energy saving approximation of Wiener process under unilateral constraints

Probability 2023-06-26 v1

Abstract

We consider the energy saving approximation of a Wiener process under unilateral constraints. We show that, almost surely, on large time intervals the minimal energy necessary for the approximation logarithmically depends on the interval's length. We also construct an adaptive approximation strategy that is optimal in a class of diffusion strategies and also provides the logarithmic order of energy consumption.

Keywords

Cite

@article{arxiv.2306.13305,
  title  = {Energy saving approximation of Wiener process under unilateral constraints},
  author = {M. A. Lifshits and S. E. Nikitin},
  journal= {arXiv preprint arXiv:2306.13305},
  year   = {2023}
}