English

Functional Meyer-Tanaka Formula

Probability 2018-06-19 v4

Abstract

The functional Ito formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. In this paper, we pursue the former type by proving the functional version of the Meyer-Tanaka Formula. Following the idea of the proof of the classical time-dependent Meyer-Tanaka formula, we study the mollification of functionals and its convergence properties. As an example, we study the running maximum and the max-martingales of Yor and Obloj.

Cite

@article{arxiv.1408.4193,
  title  = {Functional Meyer-Tanaka Formula},
  author = {Yuri F. Saporito},
  journal= {arXiv preprint arXiv:1408.4193},
  year   = {2018}
}

Comments

26 pages, 2 figures

R2 v1 2026-06-22T05:32:51.368Z