Conditional limit theorems for spectrally positive Lévy processes

Advances in Applied Probability

Volumn 34, Issue 1, 2002, Pages 158-178

  Konstantopoulos, Takis ^a   Richardson, Gregory S ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

Infinitely divisible; Large deviations; L vy process; Regular variation; Skorokhod reflection; Spectrally positive; Weak convergence

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; POISSON DISTRIBUTION; RANDOM PROCESSES;

DISCRETE-TIME RANDOM WALKS;

QUEUEING THEORY;

EID: 0036509111     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1019160955     Document Type: Article

References (25)

1. How large delays build up in a GI/G/1 queue
2. Rare events in the presence of heavy tails
3. Subexponential asymptotics for stochastic processes: Extremal behavior, stationary distributions and lust passage probabilities
4. Fluctuation theory in continuous time
5. Regular Variation
6. Diffusion approximations for open queueing networks with service interruptions
7. Conditioned limit theorems for random walks with negative drift
8. Comparing the tail of an infinitely divisible distribution with integrals of its Lévy measure
9. Estimates for the probability of rain with special emphasis on the possibility of large claims
10. The supremum distribution of a Lévy process with no negative jumps
11. Macroscopic models for long-range dependent network traffic
12. Is network traffic approximated by stable Lévy motion or fractional Brownian motion?
13. Busy periods of fractional Brownian storage: A large deviations approach
14. Unusually large values for spectrally positive stable and related processes
15. Lévy processes and infinitely divisible distributions
16. The first passage time of a level and the behavior at infinity for a class of processes with independent increments