A class of multidimensional nonlinear diffusions with the Feller property
Probability
2023-11-14 v3
Abstract
In this note we consider a family of nonlinear (conditional) expectations that can be understood as a multidimensional diffusion with uncertain drift and certain volatility. Here, the drift is prescribed by a set-valued function that depends on time and path in a Markovian way. We establish the Feller property for the associated sublinear Markovian semigroup and we observe a smoothing effect as our framework carries enough randomness. Furthermore, we link the corresponding value function to a semilinear Kolmogorov equation.
Cite
@article{arxiv.2205.15692,
title = {A class of multidimensional nonlinear diffusions with the Feller property},
author = {David Criens and Lars Niemann},
journal= {arXiv preprint arXiv:2205.15692},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2205.15200