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

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  • Forde, Martin
  • Kumar, Rohini
  • Zhang, Hongzhong

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.

Suggested Citation

  • Forde, Martin & Kumar, Rohini & Zhang, Hongzhong, 2015. "Large deviations for the boundary local time of doubly reflected Brownian motion," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 262-268.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:262-268
    DOI: 10.1016/j.spl.2014.09.004
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    Cited by:

    1. H. Dharma Kwon & Hongzhong Zhang, 2015. "Game of Singular Stochastic Control and Strategic Exit," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 869-887, October.

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