Tail behaviour of stationary solutions of random difference equations: the case of regular matrices

DOI10.1080/10236198.2011.571383zbMath1254.60071arXiv1009.1728OpenAlexW3101928688MaRDI QIDQ2902284

Gerold Alsmeyer, Sebastian Mentemeier

Publication date: 17 August 2012

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1728

zbMATH Keywords

random dynamical systemsregenerationMarkov renewal theorystochastic difference equationsHarris recurrencerandom operators and equations

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Generation, random and stochastic difference and differential equations (37H10) Renewal theory (60K05) Stochastic difference equations (39A50)

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Tails of bivariate stochastic recurrence equation with triangular matrices ⋮ CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH ⋮ On multidimensional Mandelbrot cascades ⋮ Tail indices for \(AX+B\) recursion with triangular matrices ⋮ Asymptotically linear iterated function systems on the real line ⋮ On the Kesten–Goldie constant ⋮ Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices ⋮ Componentwise different tail solutions for bivariate stochastic recurrence equations with application to ${\rm GARCH}(1,1)$ processes ⋮ Heavy tailed solutions of multivariate smoothing transforms ⋮ Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems ⋮ Random difference equations with subexponential innovations ⋮ Two-sided bounds for \(L_p\)-norms of combinations of products of independent random variables ⋮ Stable laws and spectral gap properties for affine random walks ⋮ On the tail behavior of a class of multivariate conditionally heteroskedastic processes ⋮ Affine stochastic equation with triangular matrices ⋮ Quasistochastic matrices and Markov renewal theory

Cites Work

• On the multidimensional stochastic equation \(Y_{n+1}=A_{n} Y_{n}+B_{n}\)
• Implicit renewal theory and tails of solutions of random equations
• Tail-homogeneity of stationary measures for some multidimensional stochastic recursions
• Random difference equations and renewal theory for products of random matrices
• Renewal theory for functionals of a Markov chain with general state space
• A multiplicative ergodic theorem for Lipschitz maps
• The tail of the stationary distribution of a random coefficient \(\text{AR}(q)\) model.
• A splitting technique for Harris recurrent Markov chains
• Iterated Random Functions

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