A lifetime of excursions through random walks and Lévy processes

DOI10.1007/978-3-030-83309-1_1zbMath1496.01009arXiv2112.10257OpenAlexW4212955749MaRDI QIDQ2080138

Andreas E. Kyprianou, Loïc Chaumont

Publication date: 7 October 2022

Full work available at URL: https://arxiv.org/abs/2112.10257

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) History of probability theory (60-03)

Related Items (1)

Quasi-infinite divisibility of a class of distributions with discrete part

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Erratum to: ``Asymptotic behaviour of first passage time distributions for Lévy processes
• Passage time and fluctuation calculations for subexponential Lévy processes
• Asymptotic behaviour of first passage time distributions for Lévy processes
• Large deviation results for random walks conditioned to stay positive
• Local asymptotics for the time of first return to the origin of transient random walk
• Cramér's estimate for a reflected Lévy process
• A path decomposition for Lévy processes
• Loud shot noise
• On Lévy processes conditioned to stay positive
• Almost sure relative stability of the overshoot of power law boundaries
• Asymptotic behaviour of first passage time distributions for subordinators
• Invariance principles for local times at the maximum of random walks and Lévy processes
• Right inverses of Lévy processes
• Renewal theorems and stability for the reflected process
• Corrections to ``On Lévy processes conditioned to stay positive
• On Wiener-Hopf factorisation and the distribution of extrema for certain stable processes
• On the asymptotic behaviour of first passage times for transient random walk
• Last exit times for random walks
• On the exact asymptotic behaviour of the distribution of ladder epochs
• A bivariate local limit theorem
• Thickened renewal processes
• Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion
• On the joint distribution of ladder variables of random walk
• Cramér's estimate for Lévy processes
• One-sided local large deviation and renewal theorems in the case of infinite mean
• Spitzer's condition for random walks and Lévy processes
• Moments of passage times for Lévy processes
• Some calculations for doubly perturbed Brownian motion
• Cramér's estimate for the reflected process revisited
• Perturbed Skorohod equations and perturbed reflected diffusion processes
• Small-time behaviour of {L}évy processes
• Spitzer's condition and ladder variables in random walks
• Stability and attraction to normality for Lévy processes at zero and at infinity
• Stability of the overshoot for Lévy processes
• Stochastic bounds for Lévy processes.
• On conditioning a random walk to stay nonnegative
• Upper and lower limits of doubly perturbed Brownian motion
• On distributions determined by their upward, space-time Wiener-Hopf factor
• The remainder in the renewal theorem
• The asymptotic behavior of densities related to the supremum of a stable process
• Local large deviations and the strong renewal theorem
• Curve crossing for random walks reflected at their maximum
• Local behaviour of first passage probabilities
• Passage of Lévy processes across power law boundaries at small times
• Overshoots and undershoots of Lévy processes
• Increase of Lévy processes
• Passage times of random walks and Lévy processes across power law boundaries
• Random walks crossing curved boundaries: a functional limit theorem, stability and asymptotic distributions for exit times and positions
• Windings of Planar Stable Processes
• Conditioned random walks and Lévy processes
• A Local Limit Theorem for Moderate Deviations
• A note on some results of Schuh
• Hitting Probabilities for Spectrally Positive Lévy Processes
• A note on the supremum of a stable process
• A note on conditioned random walk
• Conditional limit theorems for asymptotically stable random walks
• On the Maxima of Random Walks and Stable Processes and the Arc-Sine Law
• On higher-dimensional analogues of the arc-sine law
• A large deviation local limit theorem
• Moments of ladder heights in random walks
• Spitzer's condition for asymptotically symmetric random walk
• On the existence of the mean ladder height for random walk
• Autoregressive processes and first-hit probabilities for randomized random walks
• Asymptotic properties of supercritical branching processes I: The Galton-Watson process
• Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes
• A note on the subcritical generalized age-dependent branching process
• On single- and multi-type general age-dependent branching processes
• A note on a condition satisfied by certain random walks
• Some remarks on Brownian motion with drift
• On a formula of Takács for Brownian motion with drift
• Wiener – hopf factorization revisited and some applications
• The Martin Boundary and Ratio Limit Theorems for Killed Random Walks
• Some results involving the maximum of Brownian motion
• On the local behaviour of ladder height distributions
• A THIRD ARC-SINE THEOREM
• Overshoots over curved boundaries
• Séminaire de Probabilités XXXVIII
• Séminaire de Probabilités XXXVIII
• Overshoots over curved boundaries. II
• ON A FLUCTUATION IDENTITY FOR RANDOM WALKS AND LÉVY PROCESSES
• Some asymptotic results for transient random walks
• A FUNCTIONAL LIMIT THEOREM FOR RANDOM WALK CONDITIONED TO STAY NON-NEGATIVE
• Recurrent and transient sets for 3-dimensional random walks
• An Analogue of the Renewal Theorem in Higher Dimensions
• Hits on an axis by the simple random walk in three dimensions
• Age-dependent birth and death processes
• The progeny of a branching process
• On a functional equation for general branching processes
• A limit theorem for a class of supercritical branching processes
• Martin boundaries associated with a killed random walk
• Perturbed and non-perturbed Brownian taboo processes

This page was built for publication: A lifetime of excursions through random walks and Lévy processes