Exact and asymptotic \(n\)-tuple laws at first and last passage

DOI10.1214/09-AAP626zbMath1200.60038arXiv0811.3075OpenAlexW1835046092MaRDI QIDQ968775

Juan Carlos Pardo, Andreas E. Kyprianou, Víctor Manuel Rivero

Publication date: 6 May 2010

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.3075

zbMATH Keywords

first passage timeLévy processfluctuation theoryovershootundershootlast passage time\(n\)-tuple lawsconditioned Lévy process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40)

Related Items (21)

On Exact Sampling of Nonnegative Infinitely Divisible Random Variables ⋮ Unnamed Item ⋮ Infinite random planar maps related to Cauchy processes ⋮ Potentials of Stable Processes ⋮ Positive self-similar Markov processes obtained by resurrection ⋮ Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes ⋮ Stability of overshoots of Markov additive processes ⋮ On the Wiener-Hopf factorization for Lévy processes with bounded positive jumps ⋮ Meromorphic Lévy processes and their fluctuation identities ⋮ Explicit identities for Lévy processes associated to symmetric stable processes ⋮ Hitting distributions of \(\alpha\)-stable processes via path censoring and self-similarity ⋮ Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes ⋮ On the drawdown of completely asymmetric Lévy processes ⋮ A Wiener-Hopf Monte Carlo simulation technique for Lévy processes ⋮ A note on scale functions and the time value of ruin for Lévy insurance risk processes ⋮ Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory ⋮ Deep factorisation of the stable process III: the view from radial excursion theory and the point of closest reach ⋮ Wiener-Hopf Factorization for a Family of Lévy Processes Related to Theta Functions ⋮ On exact sampling of the first passage event of a Lévy process with infinite Lévy measure and bounded variation ⋮ First and last passage times of spectrally positive Lévy processes with application to reliability ⋮ The extended hypergeometric class of Lévy processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fluctuation theory and exit systems for positive self-similar Markov processes
• On Lévy processes conditioned to stay positive
• Fluctuation theory for Lévy processes. Ecole d'Eté de probabilités de Saint-Flour XXXV -- 2005.
• Sinaǐ's condition for real valued Lévy processes
• Some explicit identities associated with positive self-similar Markov processes
• Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
• The upper envelope of positive self-similar Markov Processes
• On moments of ladder height variables
• Classification of coharmonic and coinvariant functions for a Levy process
• A path decomposition for Markov processes
• Conditionings and path decompositions for Lévy processes
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• Ruin probabilities and overshoots for general Lévy insurance risk processes
• Stability of the overshoot for Lévy processes
• Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes
• Overshoots and undershoots of Lévy processes
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
• Passage times for a spectrally negative Lévy process with applications to risk theory
• Stochastic-Process Limits
• VOTRE LÉVY RAMPE-T-IL?
• On extreme ruinous behaviour of Lévy insurance risk processes
• The Strong Law of Large Numbers When the Mean is Undefined
• Zero-One Laws and the Minimum of a Markov Process
• Séminaire de Probabilités XXXVIII
• The Distribution of the First Hit for Stable and Asymptotically Stable Walks on an Interval
• Semi-stable Markov processes. I
• Conditioned stable Lévy processes and the Lamperti representation

This page was built for publication: Exact and asymptotic \(n\)-tuple laws at first and last passage