Renewal structure of the Brownian taut string

摘要

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.