The first passage time problem over a moving boundary for asymptotically stable Lévy processes

DOI10.1007/s10959-015-0596-xzbMath1354.60049arXiv1305.1203OpenAlexW1986473849MaRDI QIDQ325889

Tanja Kramm, Frank Aurzada

Publication date: 11 October 2016

Published in: Progress in Probability, Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1203

zbMATH Keywords

Bessel processBrownian motionmoving boundaryLévy processfirst exit timefirst-passage timeboundary crossing probabilitypersistence probabilityone-sided exit problem

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Brownian motion (60J65) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Limit theorems in probability theory (60F99)

Related Items (9)

Cramér's estimate for stable processes with power drift ⋮ The first passage time problem over a moving boundary for asymptotically stable Lévy processes ⋮ The Kolmogorov Inequality for the Maximum of the Sum of Random Variables and Its Martingale Analogues ⋮ First Passage Problems over Increasing Boundaries for Lévy Processes with Exponentially Decayed Lévy Measures ⋮ First-Passage Times over Moving Boundaries for Asymptotically Stable Walks ⋮ First-passage time asymptotics over moving boundaries for random walk bridges ⋮ Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary ⋮ Persistence Probabilities and Exponents ⋮ An Exact Asymptotics for the Moment of Crossing a Curved Boundary by an Asymptotically Stable Random Walk

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The first passage time problem over a moving boundary for asymptotically stable Lévy processes
• Suprema of Lévy processes
• Asymptotic behaviour of first passage time distributions for Lévy processes
• On the asymptotic behavior of the distributions of first-passage times. I.
• Large deviations for random walks under subexponentiality: The big-jump domain
• On the asymptotic behaviour of first passage times for transient random walk
• Time of first entry into a region with curved boundary
• Spitzer's condition for random walks and Lévy processes
• On the moments and limit distributions of some first passage times
• Moments of passage times for Lévy processes
• On the asymptotic behavior of distributions of first-passage times. II
• Small and large time stability of the time taken for a Lévy process to cross curved boundaries
• Introductory lectures on fluctuations of Lévy processes with applications.
• Passage times of random walks and Lévy processes across power law boundaries
• Some asymptotic results for transient random walks with applications to insurance risk
• Persistence Probabilities and Exponents
• An Exact Asymptotics for the Moment of Crossing a Curved Boundary by an Asymptotically Stable Random Walk
• The Crossing Time of a One-Sided Nonlinear Boundary by Sums of Independent Random Variables
• On the first hitting time and the last exit time for a Brownian motion to/from a moving boundary
• On the Brownian first-passage time over a one-sided stochastic boundary
• Brownian first exit from and sojourn over one sided moving boundary and application
• First exit densities of Brownian motion through one-sided moving boundaries
• ON ESTIMATES AND THE ASYMPTOTIC BEHAVIOR OF NONEXIT PROBABILITIES OF A WIENER PROCESS TO A MOVING BOUNDARY
• Location of Wave Fronts for the Multi-Dimensional K-P-P Equation and Brownian First Exit Densities
• Martingales, Tauberian Theorem, and Strategies of Gambling
• Some asymptotic results for transient random walks
• Asymptotics for the First Passage Times of Lévy Processes and Random Walks
• Limit theorems in fluctuation theory
• First passage times of L\'evy processes over a one-sided moving boundary
• On Moments of the Value and the Time of the First Passage over a Curvilinear Boundary
• Association of Random Variables, with Applications
• The Distribution of the First Ladder Moment and Height and Fluctuation of a Random Walk
• Asymptotics of first-passage time over a one-sided stochastic boundary

This page was built for publication: The first passage time problem over a moving boundary for asymptotically stable Lévy processes