A STOCHASTIC GRONWALL LEMMA

A simple proof of Zariski's Lemma

‎Our aim in this very short note is to show that the proof of the‎ ‎following well-known fundamental lemma of Zariski follows from an‎ ‎argument similar to the proof of the fact that the rational field‎ ‎$mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.

On Gronwall Inequality

In this paper, we obtained some new Gronwall-Bellman type integral inequalities and we give some consequences of our results.

A New Generalized Gronwall-Bellman Type Inequality

Stochastic Positive Real Lemma and Synchronization over uncertain networks

In this paper, we prove the stochastic version of the Positive Real Lemma (PRL), to study the stability problem of nonlinear systems in Lur’e form with stochastic uncertainty. We study the mean square stability problem of systems in Lur’e form with stochastic parametric uncertainty affecting the linear part of the system dynamics. The stochastic PRL result is then used to study the problem of s...

Focused Stochastic Local Search and the Lovász Local Lemma

We develop tools for analyzing focused stochastic local search algorithms. These are algorithms which search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random nearby state which, hopefully, addresses the violation without introducing many new ones. A large class of such algorithms arise from the algorithmization of ...