Two-time-scale stochastic functional differential equations with wideband noises and jumps

Yuanyuan Liu and Zhexin Wen

Chaos, Solitons & Fractals, 2024, vol. 182, issue C

Abstract: This work examines a class of path-dependent stochastic systems which are hybrid with wideband noise, Poisson jumps and a singularly perturbed Markov chain. The addition of multi-scale Markov chain allows for modeling of discrete events with both fast and slow fluctuation. While this more realistic approach presents analytical challenges due to the non-Markovian formulation resulting from the wideband noise and the singularly perturbed Markov chain. By virtue of the weak convergence method and Itô functional formula, we prove that as ɛ→0, we obtain a Markovian switching jump diffusion. Finally, we offer several examples to illustrate our findings.

Keywords: Stochastic functional differential equations; Switching jump diffusion; Wideband noise; Weak convergence; Two-time-scale; Itô functional formula (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003084

DOI: 10.1016/j.chaos.2024.114756

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