Abstract
Despite the great variety of examples introduced in Chapter I, and the equally great variety of statistical questions which arise from them, we will be able to study both with just a handful of basic tools from the theory of stochastic processes: the theory of counting processes and their intensity processes, the theory of stochastic integration, and martingale central limit theory, all centering around the mathematical concepts of martingale, predictable process, and filtration. The present chapter surveys and summarizes the basic theory as we will need it and also gives some basic mathematical material on product-integrals and functional differentiation (the functional delta-method).
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© 1993 Springer-Verlag New York, Inc.
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Andersen, P.K., Borgan, Ø., Gill, R.D., Keiding, N. (1993). The Mathematical Background. In: Statistical Models Based on Counting Processes. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4348-9_2
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DOI: https://doi.org/10.1007/978-1-4612-4348-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94519-4
Online ISBN: 978-1-4612-4348-9
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