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

Multitask diffusion adaptation over asynchronous networks