Stochastic evolutionary systems of additive functional type,
described by processes with locally
independent increments, are considered with Markov switching in an
asymptotic split state space having a stoppage state. The average and
diffusion approximation limit theorems are established in both single
and double merging. The proofs of these results are obtained using a
singular perturbation approach of linear reducible--invertible
operators and the tightness of processes. Particular cases of these
systems including integral functionals, dynamic systems, storage
processes and compound Poisson processes are also considered.
The application of limit theorems in reliability and reward
problems is discussed.
Publié le : 2004-02-14
Classification:
Stochastic evolutionary system,
Markov process with locally independent increments,
diffusion approximation,
split state space,
dynamic reliability,
reward,
60J55,
60B10,
60F17,
60K10,
60G46,
60G60
@article{1075828059,
author = {Korolyuk, Vladimir S. and Limnios, Nikolaos},
title = {Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 489-516},
language = {en},
url = {http://dml.mathdoc.fr/item/1075828059}
}
Korolyuk, Vladimir S.; Limnios, Nikolaos. Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 489-516. http://gdmltest.u-ga.fr/item/1075828059/