Stationary solutions of the stochastic differential equation \(dV_t = V_t -dU_t + dL_t\) with Lévy noise

DOI10.1016/j.spa.2010.09.003zbMath1209.60033OpenAlexW1496933810WikidataQ115341161 ScholiaQ115341161MaRDI QIDQ617912

Anita Behme, Alexander M. Lindner, Ross A. Maller

Publication date: 14 January 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2010.09.003

zbMATH Keywords

stochastic differential equationstationarityLévy processstochastic exponentialnon-causalgeneralized Ornstein-Uhlenbeck processfiltration expansion

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (17)

Markov-modulated generalized Ornstein-Uhlenbeck processes and an application in risk theory ⋮ Distributional properties of solutions of dV_t = V_t-dU_t + dL_t with Lévy noise ⋮ Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods ⋮ Stationary solutions for stochastic differential equations driven by Lévy processes ⋮ Exponential functionals of Markov additive processes ⋮ Ergodic properties of generalized Ornstein-Uhlenbeck processes ⋮ Multivariate generalized Ornstein-Uhlenbeck processes ⋮ Stationary infinitely divisible processes ⋮ Non-causal strictly stationary solutions of random recurrence equations ⋮ Continuity properties and the support of killed exponential functionals ⋮ On exponential functionals of Lévy processes ⋮ Fractional Moments of Solutions to Stochastic Recurrence Equations ⋮ On the law of killed exponential functionals ⋮ Asymmetric COGARCH processes ⋮ Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices ⋮ Second-order tail behavior for stochastic discounted value of aggregate net losses in a discrete-time risk model ⋮ On the Range of Exponential Functionals of Lévy Processes

Cites Work

• On distributional properties of perpetuities
• Continuity properties and infinite divisibility of stationary distributions of some generalized Ornstein-Uhlenbeck processes
• A note on the inhomogeneous linear stochastic differential equation.
• Stability and attraction to normality for Lévy processes at zero and at infinity
• Present value distributions with applications to ruin theory and stochastic equations
• Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes
• Ornstein–Uhlenbeck Processes and Extensions
• A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour
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