First Passage of a Markov Additive Process and Generalized Jordan Chains Articles uri icon

publication date

  • December 2010

start page

  • 1048

end page

  • 1057

issue

  • 4

volume

  • 47

international standard serial number (ISSN)

  • 0021-9002

electronic international standard serial number (EISSN)

  • 1475-6072

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. This result provides us with a technique that can be used to derive various further identities.