Spectral representations of infinitely divisible processes

DOI10.1007/BF00339998zbMath0659.60078MaRDI QIDQ1112451

Balram S. Rajput, Jan Rosiński

Publication date: 1989

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

spectral representationinfinitely divisible processesWiener-type stochastic integrals

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Stochastic integrals (60H05) Random measures (60G57)

Related Items (only showing first 100 items - show all)

Ruin probability with claims modeled by a stationary ergodic stable process. ⋮ Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations ⋮ Stationary and self-similar processes driven by Lévy processes ⋮ Limit theory for the sample autocovariance for heavy-tailed stationary infinitely divisible processes generated by conservative flows ⋮ Densities of some Poisson \(\mathbf T\)-martingales and random covering numbers ⋮ Extreme value theory for spatial random fields -- with application to a Lévy-driven field ⋮ Representations and isomorphism identities for infinitely divisible processes ⋮ On overload in a storage model, with a self-similar and infinitely divisible input. ⋮ On some extremal problems in \(H^p\) and the prediction of \(L^p\)-harmonizable stochastic processes ⋮ Some aspects of symmetric Gamma process mixtures ⋮ Estimation of continuous-time stochastic volatility models with jumps using high-frequency data ⋮ Lévy driven moving averages and semimartingales ⋮ Equivalent martingale measures for Lévy-driven moving averages and related processes ⋮ Intermittency of trawl processes ⋮ Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations ⋮ Asymptotic bounds for infinitely divisible sequences ⋮ Sample quantiles of heavy tailed stochastic processes ⋮ On Barnes beta distributions and applications to the maximum distribution of the 2D Gaussian free field ⋮ A characterization of mixing processes of type G ⋮ An ambit stochastic approach to pricing electricity forward contracts: the case of the German energy market ⋮ Volterra-type Ornstein-Uhlenbeck processes in space and time ⋮ Spectral representation of multivariate regularly varying Lévy and CARMA processes ⋮ Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes ⋮ Simple conditions for mixing of infinitely divisible processes ⋮ Multivariate CARMA processes ⋮ Uniform comparison of tails of (non-symmetric) probability measures and their symmetrized counterparts with applications ⋮ Weak drifts of infinitely divisible distributions and their applications ⋮ On the definition, stationary distribution and second order structure of positive semidefinite Ornstein-Uhlenbeck type processes ⋮ Gaussian multiplicative chaos and KPZ duality ⋮ Functional regular variation of Lévy-driven multivariate mixed moving average processes ⋮ Self-similarity and Lamperti convergence for families of stochastic processes ⋮ Integrability conditions for space-time stochastic integrals: theory and applications ⋮ Lévy processes and stochastic integrals in the sense of generalized convolutions ⋮ Extremes of Lévy driven mixed MA processes with convolution equivalent distributions ⋮ Multivariate supOU processes ⋮ Free fields associated with the relativistic operator \({-(m-\sqrt{m^{2}-\delta})}\) ⋮ High level excursion set geometry for non-Gaussian infinitely divisible random fields ⋮ A class of non-Gaussian second order random fields ⋮ Quasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes ⋮ Quasi Ornstein-Uhlenbeck processes ⋮ Brownian motion and parabolic Anderson model in a renormalized Poisson potential ⋮ On limit theory for Lévy semi-stationary processes ⋮ Stationary infinitely divisible processes ⋮ Selfdecomposability of moving average fractional Lévy processes ⋮ Random matrix models of stochastic integral type for free infinitely divisible distributions ⋮ On some dependence structures for multidimensional Lévy driven moving averages ⋮ On the oscillation of infinitely divisible and some other processes ⋮ Weak dependence and GMM estimation of supOU and mixed moving average processes ⋮ Critical Gaussian multiplicative chaos: convergence of the derivative martingale ⋮ The mild and weak solutions of a stochastic parabolic Anderson equation ⋮ Small and large scale asymptotics of some Lévy stochastic integrals ⋮ Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows ⋮ On exact scaling log-infinitely divisible cascades ⋮ Continuity properties and the support of killed exponential functionals ⋮ Numerical aspects of shot noise representation of infinitely divisible laws and related processes ⋮ Low-frequency estimation of continuous-time moving average Lévy processes ⋮ Fractional calculus and pathwise integration for Volterra processes driven by Lévy and martingale noise ⋮ On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models ⋮ A general framework for simulation of fractional fields ⋮ A theory of intermittency differentiation of 1D infinitely divisible multiplicative chaos measures ⋮ On the conditional small ball property of multivariate Lévy-driven moving average processes ⋮ Ergodic properties of stationary Poisson sequences ⋮ Selfdecomposable fields ⋮ Hybrid simulation scheme for volatility modulated moving average fields ⋮ A generalization result regarding the small and large scale behavior of infinitely divisible processes ⋮ Path and semimartingale properties of chaos processes ⋮ About atomless random measures on \(\delta \)-rings ⋮ Sample covariances of random-coefficient AR(1) panel model ⋮ On the supremum of certain families of stochastic processes ⋮ Continuity and boundedness of infinitely divisible processes: A Poisson point process approach ⋮ The class of distributions of periodic Ornstein-Uhlenbeck processes driven by Lévy processes ⋮ Estimation of the linear fractional stable motion ⋮ Stochastic expansions using continuous dictionaries: Lévy adaptive regression kernels ⋮ The domain of definition of the Lévy white noise ⋮ Limit theorems for integrated trawl processes with symmetric Lévy bases ⋮ Uniform convergence for complex [0,1-martingales] ⋮ Implicit max-stable extremal integrals ⋮ Sample paths of white noise in spaces with dominating mixed smoothness ⋮ Modeling, simulation and inference for multivariate time series of counts using trawl processes ⋮ Lévy-based growth models ⋮ Correlation cascades, ergodic properties and long memory of infinitely divisible processes ⋮ Multivariate tempered stable random fields ⋮ Polar decomposition of scale-homogeneous measures with application to Lévy measures of strictly stable laws ⋮ Wavelet analysis of the Besov regularity of Lévy white noise ⋮ Intermittency and infinite variance: the case of integrated supou processes ⋮ Power variations for fractional type infinitely divisible random fields ⋮ Completely random measures and Lévy bases in free probability ⋮ Inverse problems for regular variation of linear filters, a cancellation property for \(\sigma\)-finite measures and identification of stable laws ⋮ A constructive approach to the law equivalence of infinitely divisible random measures ⋮ Distribution tails of sample quantiles and subexponentiality ⋮ Completely random signed measures ⋮ Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes ⋮ On path properties of certain infinitely divisible processes ⋮ On nonnegative solutions of SDDEs with an application to CARMA processes ⋮ Metatimes, random measures and cylindrical random variables ⋮ Kernel estimation for Lévy driven stochastic convolutions ⋮ Multi-dimensional normal approximation of heavy-tailed moving averages ⋮ Cox point processes driven by Ornstein-Uhlenbeck type processes ⋮ Extremes of the stochastic heat equation with additive Lévy noise ⋮ Spectral representation of Gaussian semimartingales

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orlicz spaces and modular spaces
• On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals
• On stochastic integral representation of stable processes with sample paths in Banach spaces
• Ergodic properties of stationary stable processes
• Spectral representation of semistable processes, and semistable laws on Banach spaces
• On the spectral representations of complex semistable and other infinitely divisible stochastic processes
• Spreading and predictable sampling in exchangeable sequences and processes
• On the spectral representation of symmetric stable processes
• Extremes of moving averages of stable processes
• On stochastic set functions. I
• Prediction of stable processes: Spectral and moving average representations
• Harmonizable stable processes
• Random integrals of Banach space valued functions
• Some Structure Theorems for the Symmetric Stable Laws
• On stochastic set functions. II
• Random measures and harmonizable sequences
• A representation theorem for symmetric stable processes and stable measures on H

This page was built for publication: Spectral representations of infinitely divisible processes