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

Martin Forde, Rohini Kumar and Hongzhong Zhang

Statistics & Probability Letters, 2015, vol. 96, issue C, 262-268

Abstract: 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.

Keywords: Brownian motion; Large deviation; Local time (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2014.09.004

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