Asymptotic expansion for the distribution density function of the compound Poisson process in large deviations

DOI10.1007/s10959-016-0696-2zbMath1408.60023OpenAlexW2420493394MaRDI QIDQ1692251

Dovilė Deltuvienė, Aurelija Kasparavičiūtė

Publication date: 26 January 2018

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

Full work available at URL: https://doi.org/10.1007/s10959-016-0696-2

zbMATH Keywords

asymptotic expansioncompound Poisson processcumulant methodtheorems of large deviations

Mathematics Subject Classification ID

Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moderate deviations via cumulants
• Large deviations for distributions of sums of random variables: Markov chain method
• Delta method in large deviations and moderate deviations for estimators
• Cramér-type moderate deviation for Studentized compound Poisson sum
• Non-life insurance mathematics. An introduction with the Poisson process
• Asymptotic expansions for the probabilities of large deviations. Normal approximation. III
• On the rate of convergence in the local limit theorem for densities
• Large deviations of heavy-tailed sums with applications in insurance
• On approximations to generalized Poisson distributions
• Probabilities of large deviations for sums of random number of i. i. d. random variables and its application to a compound Poisson process
• Asymptotic expansion of the distribution density function for the sum of random variables in the series scheme in large deviation zones
• Convergence rate estimates in local limit theorems for Poisson random sums
• Edgeworth expansions for compound Poisson processes and the bootstrap
• Integro-Local Limit Theorems Including Large Deviations for Sums of Random Vectors. II
• An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums
• On probabilities of large claims that are compound Poisson distributed
• Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method
• Approximations for compound Poisson and Pólya processes
• Generalized Poisson Models and their Applications in Insurance and Finance
• On large deviations
• A large deviation theorem for weighted sums
• Large deviations of sums of independent random variables

This page was built for publication: Asymptotic expansion for the distribution density function of the compound Poisson process in large deviations