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- W4299285967 abstract "In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of Jordan chains associated with analytic matrix functions. Importantly, our result also provides us with a technique, which can be used to derive various further identities. We then proceed to show how to compute the stationary distribution associated with a one-sided reflected (at zero) MAP for both the spectrally positive and spectrally negative cases as well as for the two sided reflected Markov-modulated Brownian motion; these results can be interpreted in terms of queues with MAP input." @default.
- W4299285967 created "2022-10-02" @default.
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- W4299285967 date "2010-06-15" @default.
- W4299285967 modified "2023-10-18" @default.
- W4299285967 title "First passage process of a Markov additive process, with applications to reflection problems" @default.
- W4299285967 doi "https://doi.org/10.48550/arxiv.1006.2965" @default.
- W4299285967 hasPublicationYear "2010" @default.
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