Energy Saving Approximation of Wiener Process under Unilateral Constraints

Abstract

Theory of Probability &Its Applications, Volume 69, Issue 1, Page 59-70, May 2024.
We consider an 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 length. We also construct an adaptive approximation strategy optimal in a class of diffusion strategies and providing the logarithmic order of energy consumption.