Abstract:
The paper contains a detailed survey of the results on difference equations with random delays. Processes defined by them are history-dependent and can be treated as an effective modeling tool in studies of systems with strong memory, e. g. in epidemiology or population dynamics. All discussed models have simple linear form, yet many of their characteristics remain unknown. Random walks with similar history-dependent increment probabilities, of which a much more detailed description is readily available, are also briefly reviewed.
Keywords:random sequences, hereditary dynamics, history-dependent processes, random delays.
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