Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach

DOI10.1016/j.crma.2016.04.008zbMath1339.60028OpenAlexW2371614836MaRDI QIDQ292529

Nikolaos Limnios, Igor V. Samoilenko, Vladimir S. Korolyuk

Publication date: 8 June 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2016.04.008

zbMATH Keywords

weak convergencesemimartingalesadditive functionalsMarkov switchingLévy approximation schemesPoisson approximation schemes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Generalizations of martingales (60G48) Martingales with continuous parameter (60G44) Functional limit theorems; invariance principles (60F17) Local time and additive functionals (60J55) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

Differential equations with small stochastic additions under Poisson approximation conditions ⋮ Differential equations with small stochastic terms under the Lévy approximating conditions ⋮ Asymptotic dissipativity for merged stochastic evolutionary systems with Markov switchings and impulse perturbations under conditions of Lévy approximation ⋮ Asymptotic dissipativity of random processes with impulse perturbation in the Poisson approximation scheme ⋮ Control problem for the impulse process under stochastic optimization procedure and Lévy conditions ⋮ Peculiarities of construction and analysis of the information warfare model with Markov switchings and impulse perturbations under Levy approximation conditions ⋮ Asymptotic properties of the impulse perturbation process under Lévy approximation conditions with the point of equilibrium of the quality criterion ⋮ Double merging of the phase space for stochastic differential equations with small additions in Poisson approximation conditions

Cites Work

• Poisson Approximation of Processes with Locally Independent Increments with Markov Switching
• Semimartingales and Markov processes
• Poisson Approximation of Increment Processes with Markov Switching
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