# A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions

arXiv: https://arxiv.org/abs/1502.01953 · HTML: https://mlsanity.com/paper/1502.01953/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2015.

## Built on by (most cited first, 7 of 7)

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- [Stability and Convergence of Distributed Stochastic Approximations with large Unbounded Stochastic Information Delays](https://mlsanity.com/paper/2305.07091/) (2023)
- [Convergent Reinforcement Learning Algorithms for Stochastic Shortest Path Problem](https://mlsanity.com/paper/2508.13963/) (2025)

## Abstract (arXiv)

In this paper the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a differential inclusion. Two different sets of sufficient conditions are presented that guarantee the stability and convergence of stochastic recursive inclusions. Our work builds on the works of Benaim, Hofbauer and Sorin as well as Borkar and Meyn. As a corollary to one of the main theorems, a natural generalization of the Borkar and Meyn Theorem follows. In addition, the original theorem of Borkar and Meyn is shown to hold under slightly relaxed assumptions. Finally, as an application to one of the main theorems we discuss a solution to the approximate drift problem.