  The multitask diffusion LMS is an efficient strategy to simultaneously infer,
in a collaborative manner, multiple parameter vectors. Existing works on
multitask problems assume that all agents respond to data synchronously. In
several applications, agents may not be able to act synchronously because
networks can be subject to several sources of uncertainties such as changing
topology, random link failures, or agents turning on and off for energy
conservation. In this work, we describe a model for the solution of multitask
problems over asynchronous networks and carry out a detailed mean and
mean-square error analysis. Results show that sufficiently small step-sizes can
still ensure both stability and performance. Simulations and illustrative
examples are provided to verify the theoretical findings. The framework is
applied to a particular application involving spectral sensing.
