English

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.

Keywords

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

R2 v1 2026-06-24T11:34:19.548Z