Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions.

DOI10.1016/S0304-4149(03)00002-4zbMath1075.60540MaRDI QIDQ2574564

Mircea D. Grigoriu, Gennady Samorodnitsky

Publication date: 29 November 2005

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

zbMATH Keywords

stochastic differential equationMarkov processheavy tailsstationary distributioncouplingstorage processes

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (12)

Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise ⋮ The estimates of the mean first exit time from a ball for the \(\alpha \)-stable Ornstein-Uhlenbeck processes ⋮ On moments and tail behaviors of storage processes ⋮ Spectral analysis for a discrete metastable system driven by Lévy flights ⋮ Unnamed Item ⋮ Multi-scaling of moments in stochastic volatility models ⋮ Moment bounds for dissipative semimartingales with heavy jumps ⋮ First exit times of SDEs driven by stable Lévy processes ⋮ Metastable behaviour of small noise Lévy-Driven diffusions ⋮ First exit times for Lévy-driven diffusions with exponentially light jumps ⋮ Non-Gaussian limit theorem for non-linear Langevin equations driven by Lévy noise ⋮ Asymptotic properties of estimators in a stable Cox-Ingersoll-Ross model

Cites Work

• Weak limit theorems for stochastic integrals and stochastic differential equations
• Subexponential asymptotics for stochastic processes: Extremal behavior, stationary distributions and first passage probabilities
• An Extremal Problem in Probability Theory
• Storage processes with general release rule and additive inputs
• A simple coupling of renewal processes
• Subexponentiality and infinite divisibility
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