Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales

Prodhomme, Adrien

doi:10.1016/j.spa.2023.01.018

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Cited by 4 publications

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“…Approximation between Hawkes and Brownian dynamics has also been studied in [17,32], based on Komlós, Major and Tusnády (KMT) coupling techniques (see [33]). Recently, Prodhomme [58] used similar KMT coupling techniques applied to finite dimensional Markov chains and found Gaussian approximation to remain precise for very large periods of time. However these results are valid for Z d -valued continous-time Markov chains, it is unclear how they can be applied in our situation (with infinite dimension and space extension).…”

Section: Link With the Literaturementioning

confidence: 99%

Multivariate Hawkes processes on inhomogeneous random graphs

Agathe-Nerine¹

2022

Stochastic Processes and their Applications

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Section: Link With the Literaturementioning

confidence: 99%

Multivariate Hawkes processes on inhomogeneous random graphs

Agathe-Nerine¹

2022

Stochastic Processes and their Applications

View full text Add to dashboard Cite

Sharp approximation and hitting times for stochastic invasion processes

Bansaye,

Erny,

Méléard

2024

Stochastic Processes and their Applications

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Epidemic modelling by birth-death processes with spatial scaling

Arharas,

El Fatini,

Louriki

et al. 2024

J.Math.Industry

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In epidemic modeling, interpretation of compartment quantities, such as s, i, and r in relevant equations, is not always straightforward. Ambiguities regarding whether these quantities represent numbers or fractions of individuals in each compartment rise questions about significance of the involved parameters. In this paper, we address these challenges by considering a density-dependent epidemic modelling by a birth-death process approach inspired by Kurtz from 1970s’. In contrast to existing literature, which employs population size scaling under constant population condition, we scale with respect to the area. Namely, under the assumption of spatial homogeneity of the population, we consider the quantities of susceptible, infective and recovered per unit area. This spatial scaling allows diffusion approximation for birth-death type epidemic models with varying population size. By adopting this approach, we anticipate to contribute to a clear and transparent description of compartment quantities and parameters in epidemic modeling.

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Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales

Cited by 4 publications

References 23 publications

Multivariate Hawkes processes on inhomogeneous random graphs

Multivariate Hawkes processes on inhomogeneous random graphs

Sharp approximation and hitting times for stochastic invasion processes

Epidemic modelling by birth-death processes with spatial scaling

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