Since the processes involving warranty are availability, capacity, service continuity and information security, what are the processes, if any, which are involved in utility?
ITIL Planning Protection and Optimization (PPO)
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For utility we're looking at the aspects of a service that meet the functional needs of the consumer. This means that there are elements of the 4 warranty processes you have mentioned, as well as a reliance on Business Relationship Management, Service Portfolio Management, Service Catalogue Management, Service Level Management, Change Management, and also Financial Management to a certain degree.
To be honest there are very few processes that don't have an influence on the utility aspect of a service.