Abstract.
We study the asymptotic behaviour of the transition density of a Brownian motion in ?, killed at ∂?, where ?c is a compact non polar set. Our main result concern dimension d = 2, where we show that the transition density p ? t (x, y) behaves, for large t, as u(x)u(y)(t(log t)2)−1 for x, y∈?, where u is the unique positive harmonic function vanishing on (∂?)r, such that u(x) ∼ log ∣x∣.
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Received: 29 January 1999 / Revised version: 11 May 1999
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Collet, P., Martínez, S. & San Martín, J. Asymptotic behaviour of a Brownian motion on exterior domains. Probab Theory Relat Fields 116, 303–316 (2000). https://doi.org/10.1007/s004400050251
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DOI: https://doi.org/10.1007/s004400050251