Can discretely sampled financial data help us decide which continuous-time models are sensible? Diffusion processes are characterized by the continuity of their sample paths. This cannot be verified ...

Roth, A. E., and M. Sotomayor. "Stable Outcomes in Discrete and Continuous Models of Two-Sided Matching: A Unified Treatment." Revista de econometria 16, no. 2 (November 1996): 1–24.

A method to replace a continuous univariate distribution with a discrete distribution that takes MN different values is analysed. Both distributions share the same rth moments for r = 0,..., 2N - 1 ...

Split a mile in half, you get half a mile. Split the half mile, you get a quarter, and on and on, until you’ve carved out a length far smaller than the diameter of an atom. Can this slicing continue ...