# Ergodicity of robust switching control and nonlinear system of quasi variational inequalities

arXiv: https://arxiv.org/abs/1501.04477 · HTML: https://mlsanity.com/paper/1501.04477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2015.

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning for Discounted and Ergodic Control of Diffusion Processes](https://mlsanity.com/paper/2603.13155/) (2026)

## Abstract (arXiv)

We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in [3]. We prove that, as time horizon goes to infinity (resp. discount factor goes to zero) the long run average solution to the parabolic system (resp. the limiting discounted solution to the elliptic system) is characterized by a solution of a nonlinear system of ergodic variational inequalities. Our results hold under a dissipativity condition and without any non degeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments and in particular a dual randomized game representation for the solution to the system of variational inequalities.