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Stochastic Models with Power-Law Tails: The Equation X = Ax + B
Hardcover
Series: Springer Operations Research and Financial Engineering
Business GeneralEconomicsProbability & Statistics
ISBN13: 9783319296784
Publisher: Springer
Published: Jul 12 2016
Pages: 320
Weight: 1.43
Height: 0.81 Width: 6.14 Depth: 9.21
Language: English
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.
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