Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2011.14151 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous variants of the maps considered in \cite{Low}) thus extending Theorem 2.1. from that paper. We provide an Itô formula for these transforms and apply it to study of how $[f(X^n)-f(X)]\to 0$ when $X^n\to X$ (in some appropriate sense) for certain Dirichlet processes $\{X^n\}_n$, $X$ and certain locally Lipschitz continuous maps. We also consider how $[f_n(X^n)-f(X)]\to 0$ for $C^1$ maps $\{f_n\}_n$, $f$ when $f_n'\to f'$ uniformly on compacts. For applications we give examples of jump removal and stability of integrators.