The first rendezvous time of Brownian motion and compound Poisson-type processes

DOI10.1239/jap/1101840551zbMath1080.60041OpenAlexW2057695801MaRDI QIDQ4660530

David Perry, Wolfgang Stadje, Shelemyahu Zacks

Publication date: 4 April 2005

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

Full work available at URL: https://doi.org/10.1239/jap/1101840551

zbMATH Keywords

Laplace transformcompound Poisson processemptinessoverflow

Mathematics Subject Classification ID

Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (8)

On some properties of reflected skew Brownian motions and applications to dispersion in heterogeneous media ⋮ Review of some functionals of compound Poisson processes and related stopping times ⋮ The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary ⋮ First-crossing and ballot-type results for some nonstationary sequences ⋮ On the first hitting time of a one-dimensional diffusion and a compound Poisson process ⋮ On some functionals of the first passage times in jump models of stochastic volatility ⋮ On some properties of sticky Brownian motion ⋮ First Passage Times of (Reflected) Ornstein-Uhlenbeck Processes Over Random Jump Boundaries

Cites Work

• Sequential analysis. Tests and confidence intervals
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• Some results about boundary crossing for Brownian motion
• A two-sided first-exit problem for a compound Poisson process with a random upper boundary
• Boundary crossing probability for Brownian motion
• Useful martingales for stochastic storage processes with Lévy input
• Double boundary crossing result for the brownian motion
• Boundary crossing probability for Brownian motion and general boundaries
• Smoothness of first passage time distributions and a new integral equation for the first passage time density of continuous Markov processes
• A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT
• Approximations of boundary crossing probabilities for a Brownian motion
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