Ricerc@Sapienza

The purpose of this paper is to relate the notion of randomness to the granularity of the data sampled over parametrized discrete time intervals. Indeed, data defined over infinitesimal small time intervals compared to larger ones affect the randomness due to the information embedded in their granularity: larger and smaller granular intervals, as well as limit (and parametrized) intervals necessarily affect data measurements. We discuss the impact of fractionalization and data granularity on some stochastic processes widely used in finance.