Electronic Resource
Springer
Probability theory and related fields
96 (1993), S. 385-413
ISSN:
1432-2064
Keywords:
60J65
;
31A15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In a simply connected planar domainD the expected lifetime of conditioned Brownian motion may be viewed as a function on the set of hyperbolic geodesics for the domain. We show that each hyperbolic geodesic γ induces a decomposition ofD into disjoint subregions $$\Omega _j \mathop \cup \limits_j \Omega _j = D$$ and that the subregions are obtained in a natural way using Euclidean geometric quantities relating γ toD. The lifetime associated with γ on each Ω j is then shown to be bounded by the product of the diameter of the smallest ball containing γ⋂Ω j and the diameter of the largest ball in Ω j . Because this quantity is never larger than, and in general is much smaller than, the area of the largest ball in Ω j it leads to finite lifetime estimates in a variety of domains of infinite area.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01292679
Permalink
|
Location |
Call Number |
Expected |
Availability |
