Quasi sure quadratic variations of two parameter smooth martingales on the Wiener space (Q675812)

Let \(M\) be a two-parameter smooth martingale, \(\sum^n_{i,j=1} M(\Delta_{i j})^2\) be its discrete quadratic variations and \(\langle M\rangle\) be its quadratic variation process. This paper proves these processes to have quasi-sure versions and the process \(\langle M\rangle\) can be the limit of \(\sum^n_{i,j=1} M(\Delta_{ij})^2\) except on a slim set.