First-exit times for compound poisson processes for some types of positive and negative jumps

DOI10.1081/STM-120002778zbMath0998.60089OpenAlexW2062873187MaRDI QIDQ4532400

Wolfgang Stadje, Shelemyahu Zacks, David Perry

Publication date: 25 November 2002

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/stm-120002778

zbMATH Keywords

compound Poisson processsingle-server queuefirst-exit time

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25)

Related Items (30)

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Cites Work

• Sequential analysis. Tests and confidence intervals
• On the discounted penalty at ruin in a jump-diffusion and the perpetual put option
• The moments of ruin time in the classical risk model with discrete claim size distribution
• Explicit finite-time and infinite-time ruin probabilities in the continuous case
• Inequality extensions of Prabhu's formula in ruin theory
• On the first crossing of the surplus process with a given upper barrier
• Firm behaviour under the threat of liquidation
• Wiener-Hopf analysis of an M/G/1 queue with negative customers and of a related class of random walks
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• Analysis of a defective renewal equation arising in ruin theory
• Risk analysis for a stochastic cash manangement model with two type of customers
• Contributions to the theory of first-exit times of some compound processes in queueing theory
• Impulse Control of Brownian Motion
• A Pollaczek–Khintchine formula for M/G/1 queues with disasters
• Queues with negative arrivals
• Distributions of stopping times for poisson processes with linear boundaries
• Useful martingales for stochastic storage processes with Lévy input
• On cycle maxima, first passage problems and extreme value theory for queues
• Distribution of first-exit times for empirical counting and poisson processes with moving boundaries
• Distributions of stopping times for compound poisson processes with positive jumps and linear boundaries
• The probability of ruin in finite time with discrete claim size distribution
• Absorption and first-passage times for a compound Poisson process in a general upper boundary
• Performance analysis of sequential tests between Poisson processes
• The moment generating function of the stopping time for a linearly stopped poisson process
• First-exit times for increasing compound processes
• First crossing of basic counting processes with lower non-linear boundaries: A unified approach through pseudopolynomials (I)
• The M/G/1 queue with negative customers
• The Workload in the M/G/1 Queue with Work Removal
• A Note on Negative Customers, GI/G/1 Workload, and Risk Processes
• On the Time Value of Ruin
• Sequential Decision Problems for Processes with Continuous time Parameter. Testing Hypotheses

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