In applications, and especially in mathematical finance, random
time-dependent events are often modeled as stochastic processes.
Assumptions are made about the structure of such processes, and serious
researchers will want to justify those assumptions through the use of
data. As statisticians are wont to say, "In God we trust; all others
must bring data."
This book establishes the theory of how to go about estimating not just
scalar parameters about a proposed model, but also the underlying
structure of the model itself. Classic statistical tools are used: the
law of large numbers, and the central limit theorem. Researchers have
recently developed creative and original methods to use these tools in
sophisticated (but highly technical) ways to reveal new details about
the underlying structure. For the first time in book form, the authors
present these latest techniques, based on research from the last 10
years. They include new findings.
This book will be of special interest to researchers, combining the
theory of mathematical finance with its investigation using market data,
and it will also prove to be useful in a broad range of applications,
such as to mathematical biology, chemical engineering, and physics.