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

Author

Listed:
  • Aleksian, Ashot
  • Villeneuve, Stéphane

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.

Suggested Citation

  • Aleksian, Ashot & Villeneuve, Stéphane, 2025. "Freidlin-Wentzell type exit-time estimates for time-inhomogeneous diffusions and their applications," TSE Working Papers 25-1612, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:130135
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