Lifshits, Mikhail; Setterqvist, Eric - In: Stochastic Processes and their Applications 125 (2015) 2, pp. 401-427
Let W be a Wiener process. For r0 and T0 let IW(T,r)2 denote the minimal value of the energy ∫0Th′(t)2dt taken among all absolutely continuous functions h(⋅) defined on [0,T], starting at zero and satisfying W(t)−r≤h(t)≤W(t)+r,0≤t≤T. The function minimizing energy is a taut...