Some limit theorems for simple point processes (a martingale approach)

DOI10.1080/17442508008833145zbMath0441.60045OpenAlexW2056955295MaRDI QIDQ3883235

Albert N. Shiryaev, Robert Sh. Liptser, Youri M.Kabanov

Publication date: 1980

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442508008833145

zbMATH Keywords

exponential formulacompensatordistributional convergence

Mathematics Subject Classification ID

Martingales with continuous parameter (60G44) General theory of stochastic processes (60G07) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (12)

On properties of strong solutions of stochastic equations with respect to semimartingales ⋮ Convergence of thinning processes using compensators ⋮ On the convergence of point processes ⋮ Poisson approximation for some point processes in reliability ⋮ Convergence of probability measures and Markov decision models with incomplete information ⋮ On convergence in variation of the distributions of multivariate point processes ⋮ Convergence of the empirical distribution to the poisson process ⋮ Unnamed Item ⋮ Stochastic equations and krylov's estimates for semimartingales ⋮ Compensators and Cox convergence ⋮ Necessary and sufficient conditions for the convergence of semimartingales to processes with conditionally independent increments ⋮ Stability theorem for stochastic differential equations with jumps

Cites Work

• Unnamed Item
• A martingale approach to the Poisson convergence of simple point processes
• Processus ponctuels et martingales: résultats récents sur la modélisation et le filtrage

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