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Books > Business & Economics > Economics > Economic theory & philosophy
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Stochastic Models with Power-Law Tails - The Equation X = AX + B (Hardcover, 1st ed. 2016)
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Stochastic Models with Power-Law Tails - The Equation X = AX + B (Hardcover, 1st ed. 2016)
Series: Springer Series in Operations Research and Financial Engineering
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In this monograph the authors give a systematic approach to the
probabilistic properties of the fixed point equation X=AX+B. A
probabilistic study of the stochastic recurrence equation
X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables
A_t, where (A_t,B_t) constitute an iid sequence, is provided. The
classical theory for these equations, including the existence and
uniqueness of a stationary solution, the tail behavior with special
emphasis on power law behavior, moments and support, is presented.
The authors collect recent asymptotic results on extremes, point
processes, partial sums (central limit theory with special emphasis
on infinite variance stable limit theory), large deviations, in the
univariate and multivariate cases, and they further touch on the
related topics of smoothing transforms, regularly varying sequences
and random iterative systems. The text gives an introduction to the
Kesten-Goldie theory for stochastic recurrence equations of the
type X_t=A_tX_{t-1}+B_t. It provides the classical results of
Kesten, Goldie, Guivarc'h, and others, and gives an overview of
recent results on the topic. It presents the state-of-the-art
results in the field of affine stochastic recurrence equations and
shows relations with non-affine recursions and multivariate regular
variation.
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