Freidlin-Wentzell type exit-time estimates for time-inhomogeneous diffusions and their applications

Ashot Aleksian and Stéphane Villeneuve

No 25-1612, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and diffusion terms are uniformly close to some time-independent functions, the exit time grows exponentially both in probability and in $L_1$ as a parameter that controls the noise tends to zero. We also characterize the exit position of the time-inhomogeneous process. Additionally, we investigate the impact of relaxing the uniform closeness condition on the exit-time behavior. As an application, we extend these results to the McKean-Vlasov process. Our findings improve upon existing results in the literature for the exit-time problem for this class of processes.

Keywords: Freidlin-Wentzell theory; time-inhomogeneous diffusion; McKean-Vlasov process; exit time (search for similar items in EconPapers)
Date: 2025-01
New Economics Papers: this item is included in nep-mac
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Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:130135

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