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January 21, 2026Queueing SystemsOpen Access

The strong law of large numbers and a functional central limit theorem for general markov additive processes

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The aim is to explore the strong law of large numbers and central limit theorem for Markov additive processes with general modulating processes.
Revisits fundamental questions regarding MAPs with conditional stationary increments.
Examines ergodic theorem for additive functionals.
Considers positive or null-recurrent modulating processes.
Demonstrates a strong law of large numbers applicable to general Markov processes.
Presents a CLT-type result inspired by the proposed methodology.

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Implication

This note demonstrates the strong law of large numbers and central limit theorem for Markov additive processes, suggesting broader applicability in stochastic modeling.

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Kyprianou et al. (2026) studied this question.

synapsesocial.com/papers/69706c87b6488063ad5c19ae https://doi.org/10.1007/s11134-025-09963-0

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Implication

This note demonstrates the strong law of large numbers and central limit theorem for Markov additive processes, suggesting broader applicability in stochastic modeling.

The strong law of large numbers and a functional central limit theorem for general markov additive processes

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Discussion

Implication

Cite This Study

The strong law of large numbers and a functional central limit theorem for general markov additive processes

Key Points

Discussion

Implication

Cite This Study

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