Strongly Convergent Homogeneous Approximations to Inhomogeneous Markov Jump Processes and Applications
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Strongly Convergent Homogeneous Approximations to Inhomogeneous Markov Jump Processes and Applications. / Bladt, Martin; Peralta, Oscar.
I: Mathematics of Operations Research, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Strongly Convergent Homogeneous Approximations to Inhomogeneous Markov Jump Processes and Applications
AU - Bladt, Martin
AU - Peralta, Oscar
PY - 2024
Y1 - 2024
N2 - The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial mathematical burden which is usually circumvented by using well-known generic distributional approximations or simulations. This article provides a novel approximation method that tailors the dynamics of a time-homogeneous Markov jump process to meet those of its time-inhomogeneous counterpart on an increasingly fine Poisson grid. Strong convergence of the processes in terms of the Skorokhod J1 metric is established, and convergence rates are provided. Under traditional regularity assumptions, distributional convergence is established for unconditional proxies, to the same limit. Special attention is devoted to the case where the target process has one absorbing state and the remaining ones transient, for which the absorption times also converge. Some applications are outlined, such as univariate hazard-rate density estimation, ruin probabilities, and multivariate phase-type density evaluation.
AB - The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial mathematical burden which is usually circumvented by using well-known generic distributional approximations or simulations. This article provides a novel approximation method that tailors the dynamics of a time-homogeneous Markov jump process to meet those of its time-inhomogeneous counterpart on an increasingly fine Poisson grid. Strong convergence of the processes in terms of the Skorokhod J1 metric is established, and convergence rates are provided. Under traditional regularity assumptions, distributional convergence is established for unconditional proxies, to the same limit. Special attention is devoted to the case where the target process has one absorbing state and the remaining ones transient, for which the absorption times also converge. Some applications are outlined, such as univariate hazard-rate density estimation, ruin probabilities, and multivariate phase-type density evaluation.
U2 - 10.1287/moor.2022.0153
DO - 10.1287/moor.2022.0153
M3 - Journal article
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
SN - 0364-765X
ER -
ID: 384353003