Suprema and sojourn times of Lévy processes with exponential tails

DOI10.1016/S0304-4149(97)00031-8zbMath0915.60050MaRDI QIDQ1275930

Michael Braverman

Publication date: 14 January 1999

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

zbMATH Keywords

exponential distributionsLévy processsojourn times

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) General theory of stochastic processes (60G07)

Related Items (13)

Suprema of compound Poisson processes with light tails. ⋮ Stability of the exit time for Lévy processes ⋮ Convolution equivalent Lévy processes and first passage times ⋮ Sojourn measures of Student and Fisher-Snedecor random fields ⋮ Formula for the supremum distribution of a spectrally positive \(\alpha \)-stable Lévy process ⋮ A NOTE ON THE CLOSURE OF CONVOLUTION POWER MIXTURES (RANDOM SUMS) OF EXPONENTIAL DISTRIBUTIONS ⋮ Path decomposition of ruinous behavior for a general Lévy insurance risk process ⋮ On a class of Lévy processes ⋮ Finite time ruin probabilities for tempered stable insurance risk processes ⋮ On the asymptotic behaviour of Lévy processes. I: Subexponential and exponential processes ⋮ Heavy tails of a Lévy process and its maximum over a random time interval ⋮ Remarks on suprema of Lévy processes with light tailes ⋮ Asymptotic Ruin Probabilities of the Lévy Insurance Model under Periodic Taxation

Cites Work

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• Convolution tails, product tails and domains of attraction
• The supremum of a process with stationary independent and symmetric increments
• On the supremum of an infinitely divisible process
• On convolution tails
• The class of subexponential distributions
• Functions of probability measures
• Functionals of infinitely divisible stochastic processes with exponential tails
• 𝜉-radial processes and random Fourier series
• Some asymptotic results for transient random walks
• Convergence of stochastic processes

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