This paper is concerned with elliptic equations satisfied by the mean first exit time of a stochastic process and higher moments. We prove an estimate for all moments of the first exit time in a cylindrical domain, using viscosity solutions. As a further result, we show the existence and the uniqueness of a more general fully nonlinear Dirichlet problem for partial trace equations, which can be associated to nonlinear diffusion.
Alexandroff-Bakelman-Pucci estimate and first exit time in cylindrical domains
Antonio Vitolo
2026
Abstract
This paper is concerned with elliptic equations satisfied by the mean first exit time of a stochastic process and higher moments. We prove an estimate for all moments of the first exit time in a cylindrical domain, using viscosity solutions. As a further result, we show the existence and the uniqueness of a more general fully nonlinear Dirichlet problem for partial trace equations, which can be associated to nonlinear diffusion.File in questo prodotto:
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