Stochastic Models With Power-law Tails: The Equation X = Ax + B (springer Series In Operations Research And Financial Engineering)
by Thomas Mikosch /
2016 / English / PDF
3.5 MB Download
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.
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.
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.