Regenerative renewal processes

Regenerative Processes

We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d. cycles. Although we focus on the classical definition, we present a more general definition that allows for some form of dependence between two adjacent cycles, and mention two further extensions of the second definition. We mention the connection of regenerative processes to...

On Transient Regenerative Processes

Regenerative tree growth processes

We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n ≥ 1, with a regenerative property at branch points. We establish necessary and sufficient conditions on the growth rules under which we can apply results by Haas and Miermont to establish self-similar random trees and residual mass processes as scaling limits. This framework includes...

Random fuzzy alternating renewal processes

Random fuzzy theory offers an appropriate mechanism to model random fuzzy phenomena, with a random fuzzy variable defined as a function from a credibility space to a collection of random variables. Based on this theory, this paper presents the results of an investigation into the representation of properties of alternating renewal processes that are described by sequences of positive random fuz...

Intrusions in Marked Renewal Processes

We present a probabilistic model of an intrusion in a marked renewal process. Given a process and a sequence of events, an intrusion is a subsequence of events that is not produced by the process. Applications of the model are, for example, online payment fraud with the fraudster taking over a user’s account and performing payments on the user’s behalf, or unexpected equipment failures due to u...