Abstract
In contrast to the preceding chapters, where we considered the propagation of wanted messages over the telecommunication system, we now turn to the propagation of unwanted ones, e.g., of malware . We introduce, on the set Φ = (X i)i ∈ I of all the device locations, a time-dependent Markovian model of the set of infected devices, evolving in time as a stochastic process. The main random mechanism that drives this infection process has two elements: (1) each device that has an infected neighbor is also infected after an exponentially distributed random time, and (2) any infected device either remains infected, or it undergoes a spontaneous healing, or it becomes patched by some neighboring device of another type, again after independent exponentially distributed random times.
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- 1.
The definition of separability of a Markov chain is very technical; it ensures that the paths t↦ω(t) are not too ‘wild’. We decided not to give this definition here.
- 2.
Then the collection of these transition probabilities is called standard .
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Jahnel, B., König, W. (2020). Random Malware Propagation: Interacting Markov Processes. In: Probabilistic Methods in Telecommunications. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36090-0_8
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