No CrossRef data available.
Article contents
PDE for the joint law of the pair of a continuous diffusion and its running maximum
Published online by Cambridge University Press: 10 July 2023
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 $\big(M_t,X_t\big)$ is a weak solution of a Fokker–Planck partial differential equation on the closed set $\big\{(m,x)\in \mathbb{R}^{d+1},\,{m\geq x^1}\big\},$ using an integral expansion of this density.
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust