ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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∣.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004400050251
Permalink