Summary
We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for each of the following classes of domains:L p-domains (p=n−1), uniformly regular twistedL p-domains (p=n−1), and twisted Hölder domains (α=1/3). A related parabolic boundary Harnack principle is proved.
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Bass, R.F., Burdzy, K. Lifetimes of conditioned diffusions. Probab. Th. Rel. Fields 91, 405–443 (1992). https://doi.org/10.1007/BF01192065
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DOI: https://doi.org/10.1007/BF01192065