Discretization of processes

Abstract

In applications, and especially in mathematical finance, random time-dependentevents are often modeled as stochastic processes. Assumptions aremade about the structure of such processes, and serious researcherswill want to justify those assumptions through the use of data.As statisticians are wont to say, “In God we trust; all others mustbring data.” This book establishes the theory of how to go aboutestimating not just scalar parameters about a proposed model, butalso the underlying structure of the model itself. Classic statisticaltools are used: the law of large numbers, and the central limit theorem. Researchershave recently developed creative and original methods to use thesetools in sophisticated (but highly technical) ways to reveal newdetails about the underlying structure. For the first time in bookform, the authors present these latest techniques, based on researchfrom the last 10 years. They include new findings.This book will be of special interest to researchers, combining thetheory of mathematical finance with its investigation using marketdata, and it will also prove to be useful in a broad range of applications,such as to mathematical biology, chemical engineering, and physics.