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Renewal structure of the Brownian taut string

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  • Schertzer, Emmanuel

Abstract

In a recent paper Lifshits and Setterqvist (2015), M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion w, defined as the function of minimal quadratic energy on [0,T] staying in a tube of fixed width h>0 around w. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time T.

Suggested Citation

  • Schertzer, Emmanuel, 2018. "Renewal structure of the Brownian taut string," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 487-504.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:2:p:487-504
    DOI: 10.1016/j.spa.2017.05.004
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    References listed on IDEAS

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    1. Miller, Douglas R., 1974. "Limit theorems for path-functionals of regenerative processes," Stochastic Processes and their Applications, Elsevier, vol. 2(2), pages 141-161, April.
    2. Lifshits, Mikhail & Setterqvist, Eric, 2015. "Energy of taut strings accompanying Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 401-427.
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