Finding an NARE whose minimal nonnegative solution represents first-passage increments in two-dimensional Markov modulated Brownian motion

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The derived Laplace-Stieltjes transform addresses first-passage increments in Markov processes, revealing fundamental insights.
A matrix exponential function represents the transform matrix via a minimal nonnegative solution of a nonsymmetric algebraic Riccati equation.
This research employs an innovative approach in dealing with two-dimensional Brownian motion in continuous-time Markov processes.
Understanding this transform can enhance the modeling of complex stochastic systems like financial markets or queueing models.

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Analysis reveals the Laplace-Stieltjes transform for increments in a Markov-modulated process, indicating new insights into stochastic modeling.

Ryu et al. (2025) studied this question.

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Analysis reveals the Laplace-Stieltjes transform for increments in a Markov-modulated process, indicating new insights into stochastic modeling.