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<p>The computation of the pair of matrices describing the first passage time of a Markov additive process is considered. This pair of matrices is characterized as a solution to an integral matrix equation for which we develop an iterative method. At each step, it requires computing the extremal solution to a mixed linear-quadratic matrix equation, which is accomplished by a quadratically convergent algorithm. When all the jumps are of phase-type distribution, the integral matrix equation can be transformed into a single mixed linear-quadratic matrix equation and thus the pair of matrices can be computed with quadratic convergence.</p>

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Computation of First Passage of Markov Additive Processes

  • 期刊论文

  • 发表日期：

    2025年4月19日

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  • Changli Liu,
  • Jungong Xue,
  • Junxin Zhang

摘要

The computation of the pair of matrices describing the first passage time of a Markov additive process is considered. This pair of matrices is characterized as a solution to an integral matrix equation for which we develop an iterative method. At each step, it requires computing the extremal solution to a mixed linear-quadratic matrix equation, which is accomplished by a quadratically convergent algorithm. When all the jumps are of phase-type distribution, the integral matrix equation can be transformed into a single mixed linear-quadratic matrix equation and thus the pair of matrices can be computed with quadratic convergence.