This paper presents an overview of stochastic stability methods, mostly motivated by (but not limited to) stochastic network applications. We work with stochastic recursive sequences, and, in particular, Markov chains in a general Polish state space. We discuss, and frequently compare, methods based on (i) Lyapunov functions, (ii) fluid limits, (iii) explicit coupling (renovating events and Har...

Consider a large collection of similar gravitational wave sources. If we cannot resolve the individual signals produced by these sources and know only their statistical properties, the signals form a stochastic background. We group stochastic backgrounds into the following two classes: those for which the individual sources have (i) average redshift z ≫ 1 and (ii) average redshift z ∼ 1. Typica...

We study regularized stochastic convex optimization subject to linear equality constraints. This class of problems was recently also studied by Ouyang et al. (2013) and Suzuki (2013); both introduced similar stochastic alternating direction method of multipliers (SADMM) algorithms. However, the analysis of both papers led to suboptimal convergence rates. This paper presents two new SADMM method...