2014/07/13 by Franco Flandoli, Flandoli, Franco, Michael A. Högele +1
Economics, Econometrics and Finance · Engineering · Decision Sciences · #Stochastic processes and financial applications #Stability and Controllability of Differential Equations #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1407.3469
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an α-stable process. It is proved that extremal solutions are selected and the respective probability of selection is computed. For this purpose an exit time problem from the half-line, which is of interest in its own right, is formulated and studied by means of a suitable decomposition in small and large jumps adapted to the singular drift.