Large deviations for the boundary local time of doubly reflected Brownian motion

We compute a closed-form expression for the moment generating function fˆ(x;λ,α)=1λEx(eαLτ), where Lt is the local time at zero for standard Brownian motion with reflecting barriers at 0 and b, and τ∼Exp(λ) is independent of W. By analyzing how and where fˆ(x;⋅,α) blows up in λ, a large-time large deviation principle (LDP) for Lt/t is established using a Tauberian result and the Gärtner–Ellis Theorem.

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Year of publication:	2015
Authors:	Forde, Martin ; Kumar, Rohini ; Zhang, Hongzhong
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 96.2015, C, p. 262-268
Publisher:	Elsevier
Subject:	Brownian motion \| Large deviation \| Local time

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10011115949