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math.PR2026
Multi-time Markov renewal chains and stratified renewal theorems
Leonidas Kordalis, Samis Trevezas
We develop stratified renewal theorems for multi-time observations of Markov-additive paths on standard Borel state spaces with nonnegative integer vector increments. Horizon direc…
math.PR2026
Discrete time-multidimensional renewal theory and applications
Leonidas Kordalis, Samis Trevezas
We develop a discrete-time renewal framework in which renewal events evolve along multiple time coordinates and the sojourn mechanism is described by a general distribution on the…
math.PR2025
Time multidimensional Markov Renewal chains -- An algebraic approach
Leonidas Kordalis, Samis Trevezas
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Mark…