Regular variation in the tail behaviour of solutions of random difference equations
From MaRDI portal
Publication:1327610
DOI10.1214/aoap/1177005205zbMath0802.60057OpenAlexW2076197047MaRDI QIDQ1327610
Publication date: 12 December 1994
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aoap/1177005205
regular variationmoment conditionsrandom equationrandom environment branching processesrandom recurrence relationupper tail
Random operators and equations (aspects of stochastic analysis) (60H25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
Related Items (55)
On Cramér-like asymptotics for risk processes with stochastic return on investments ⋮ Finite and infinite time ruin probabilities in a stochastic economic environment. ⋮ Importance sampling for maxima on trees ⋮ Random recurrence equations and ruin in a Markov-dependent stochastic economic environment ⋮ On stochastic difference equations in insurance ruin theory ⋮ Tail-homogeneity of stationary measures for some multidimensional stochastic recursions ⋮ Tails of bivariate stochastic recurrence equation with triangular matrices ⋮ The random difference equation \(X_ n = A_ n X_{n-1} + B_ n\) in the critical case ⋮ A large deviations approach to limit theory for heavy-tailed time series ⋮ Regular Variation of Infinite Series of Processes with Random Coefficients ⋮ Distribution tails of a history-dependent random linear recursion ⋮ Interplay of financial and insurance risks in dependent discrete-time risk models ⋮ Asymptotics for a discrete-time risk model with Gamma-like insurance risks ⋮ Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks ⋮ A revisit to ruin probabilities in the presence of heavy-tailed insurance and financial risks ⋮ Tail asymptotics for exponential functionals of Lévy processes: the convolution equivalent case ⋮ On the joint tail behavior of randomly weighted sums of heavy-tailed random variables ⋮ An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity ⋮ On random coefficient INAR(1) processes ⋮ Asymptotic independence ex machina: Extreme value theory for the diagonal SRE model ⋮ Iterated random functions and slowly varying tails ⋮ Tail behavior of solutions of linear recursions on trees ⋮ Multivariate linear recursions with Markov-dependent coefficients ⋮ Renorming divergent perpetuities ⋮ Infinite-time absolute ruin in dependent renewal risk models with constant force of interest ⋮ Random linear recursions with dependent coefficients ⋮ Interplay of insurance and financial risks in a stochastic environment ⋮ Asymptotics for ruin probabilities in Lévy-driven risk models with heavy-tailed claims ⋮ Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems ⋮ Multivariate Markov-switching ARMA processes with regularly varying noise ⋮ One-dimensional linear recursions with Markov-dependent coefficients ⋮ Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps ⋮ Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments ⋮ On invariant measures of stochastic recursions in a critical case ⋮ Random difference equations with subexponential innovations ⋮ The probabilities of absolute ruin in the renewal risk model with constant force of interest ⋮ Extremes of a class of deterministic sub-sampled processes with applications to stochastic difference equations ⋮ On perpetuities with gamma-like tails ⋮ Tail Asymptotics of the Supremum of a Regenerative Process ⋮ Iterated random functions and regularly varying tails ⋮ Integrated insurance risk models with exponential Lévy investment ⋮ Tail probabilities for infinite series of regularly varying random vectors ⋮ Interplay of insurance and financial risks in a discrete-time model with strongly regular variation ⋮ Importance sampling of heavy-tailed iterated random functions ⋮ On perpetuities with light tails ⋮ Stochastic recursions: between Kesten's and Grincevičius-Grey's assumptions ⋮ A law of large numbers and central limit theorem for the logarithm of an autoregressive process with a stationary driving sequence ⋮ Random walks in a moderately sparse random environment ⋮ The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks ⋮ Slowly varying asymptotics for signed stochastic difference equations ⋮ Affine stochastic equation with triangular matrices ⋮ Stochastic fixed-point equation and local dependence measure ⋮ Perpetuities with thin tails revisited ⋮ Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovations ⋮ On supercritical branching processes with emigration
This page was built for publication: Regular variation in the tail behaviour of solutions of random difference equations