Numerical approximations and convergence analysis of piecewise diffusion Markov processes, with application to glioma cell migration

Evelyn Buckwar and Amira Meddah

Applied Mathematics and Computation, 2025, vol. 491, issue C

Abstract: In this paper, we focus on numerical approximations of Piecewise Diffusion Markov Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our approach is based on the thinning method for modelling the jump mechanism and combines the Euler-Maruyama scheme to approximate the underlying flow dynamics. For the proposed approximation schemes, we study both the mean-square and weak convergence. Weak convergence of the algorithms is established by a martingale problem formulation. Moreover, we employ these results to simulate the migration patterns exhibited by moving glioma cells at the microscopic level. Further, we develop and implement a splitting method for this PDifMP model and employ both the Thinned Euler-Maruyama and the splitting scheme in our simulation example, allowing us to compare both methods.

Keywords: Piecewise diffusion Markov processes; Thinning method; Splitting method; Low-grade glioma model (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:491:y:2025:i:c:s0096300324006945

DOI: 10.1016/j.amc.2024.129233

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