ISSN:
1432-2064
Keywords:
Mathematics Subject Classification (1991): 58G32, 60J15, 60J60, 60J65
;
Key words: Brownian bridge – Symmetric space – Tree – Excursion – Hyperbolic Space – Reflected random walk – Reflected Brownian motion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let B be the Brownian motion on a noncompact non Euclidean rank one symmetric space H. A typical examples is an hyperbolic space H n , n 〉 2. For ν 〉 0, the Brownian bridge B (ν) of length ν on H is the process B t , 0 ≤t≤ν, conditioned by B 0 = B ν = o, where o is an origin in H. It is proved that the process converges weakly to the Brownian excursion when ν→ + ∞ (the Brownian excursion is the radial part of the Brownian Bridge on ℝ3). The same result holds for the simple random walk on an homogeneous tree.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004400050237
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