Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime

DOI10.1017/apr.2021.16zbMath1475.60072OpenAlexW3215097728MaRDI QIDQ5013251

Bo Li, Guodong Pang

Publication date: 29 November 2021

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

Full work available at URL: https://doi.org/10.1017/apr.2021.16

zbMATH Keywords

shot noise processinfinite-server queuesdependent noises(dependent) random delays of arrivalscluster arrivalGaussian limit processeslarge-intensity asymptotic regime

Mathematics Subject Classification ID

Gaussian processes (60G15) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Sample path properties (60G17) Generalized stochastic processes (60G20)

Related Items (1)

Functional limit theorems for nonstationary marked Hawkes processes in the high intensity regime

Cites Work

• Unnamed Item
• Unnamed Item
• Moment convergence of first-passage times in renewal theory
• Asymptotics of random processes with immigration. I: Scaling limits.
• Asymptotics of random processes with immigration. II: Convergence to stationarity.
• Bivariate distributions with given marginals
• Regular variation in the mean and stable limits for Poisson shot noise
• Functional limit theorems for a new class of non-stationary shot noise processes
• Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds
• Explosive Poisson shot noise processes with applications to risk reserves
• Crossings of smooth shot noise processes
• Two-parameter heavy-traffic limits for infinite-server queues with dependent service times
• A functional limit theorem for random processes with immigration in the case of heavy tails
• Functional limit theorems for renewal shot noise processes with increasing response functions
• Hitting times for Gaussian processes
• Fractional Brownian motion as a weak limit of Poisson shot noise processes -- with applications to finance
• Weak convergence of compound stochastic process. I
• Shot noise on cluster processes with cluster marks, and studies of long range dependence
• Stochastic-Process Limits
• A note on convergence to stationarity of random processes with immigration
• Renewal Theory for Perturbed Random Walks and Similar Processes
• INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES
• The central limit theorem for the Poisson shot-noise process
• Normal convergence of multidimensional shot noise and rates of this convergence
• A shot process by burst properties
• On generalized shot noise
• The Berry-Esseen bound for the Poisson shot-noise
• Extremal properties of shot noise processes
• An Introduction to the Theory of Point Processes
• Weak convergence of random processes with immigration at random times
• A functional limit theorem for general shot noise processes
• Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises
• On the total claim amount for marked Poisson cluster models
• High density shot noise and gaussianity

This page was built for publication: Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime