Stochastic Limit Theory, published in 1994, has become a standard
reference in its field. Now reissued in a new edition, offering
updated and improved results and an extended range of topics,
Davidson surveys asymptotic (large-sample) distribution theory with
applications to econometrics, with particular emphasis on the
problems of time dependence and heterogeneity. The book is designed
to be useful on two levels. First, as a textbook and reference
work, giving definitions of the relevant mathematical concepts,
statements, and proofs of the important results from the
probability literature, and numerous examples; and second, as an
account of recent work in the field of particular interest to
econometricians. It is virtually self-contained, with all but the
most basic technical prerequisites being explained in their
context; mathematical topics include measure theory, integration,
metric spaces, and topology, with applications to random variables,
and an extended treatment of conditional probability. Other
subjects treated include: stochastic processes, mixing processes,
martingales, mixingales, and near-epoch dependence; the weak and
strong laws of large numbers; weak convergence; and central limit
theorems for nonstationary and dependent processes. The functional
central limit theorem and its ramifications are covered in detail,
including an account of the theoretical underpinnings (the weak
convergence of measures on metric spaces), Brownian motion, the
multivariate invariance principle, and convergence to stochastic
integrals. This material is of special relevance to the theory of
cointegration. The new edition gives updated and improved versions
of many of the results and extends the coverage of many topics, in
particular the theory of convergence to alpha-stable limits of
processes with infinite variance.
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