PDE for the joint law of the pair of a continuous diffusion and its running maximum
Probability
2023-01-09 v1
Abstract
Let X be a d-dimensional diffusion and M the running supremum of its first component. In this paper, we show that for any t > 0, the density (with respect to the d + 1-dimensional Lebesgue measure) of the pair (Mt, Xt) is a weak solution of a Fokker-Planck partial differential equation on the closed set {(m, x) R d+1, m x 1}, using an integral expansion of this density.
Cite
@article{arxiv.2301.02442,
title = {PDE for the joint law of the pair of a continuous diffusion and its running maximum},
author = {Laure Coutin and Monique Pontier},
journal= {arXiv preprint arXiv:2301.02442},
year = {2023}
}