Let $\mu^n$ be the distribution of a product of $n$ independent identically distributed random matrices. We study tightness and convergence of the sequence $\{\mu^n, n \geq 1\}$. We apply this to linear stochastic differential (and difference) equations, characterize the stability in probability, in the sense of Hashminski, of the zero solution, and find all their stationary solutions.
Publié le : 1987-01-14
Classification:
Products of random matrices,
linear stochastic systems,
stability in probability,
stationary solution,
convergence in distribution,
linear stochastic differential equations,
60B15,
60B10,
60H10,
60H25
@article{1176992256,
author = {Bougerol, Philippe},
title = {Tightness of Products of Random Matrices and Stability of Linear Stochastic Systems},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 40-74},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992256}
}
Bougerol, Philippe. Tightness of Products of Random Matrices and Stability of Linear Stochastic Systems. Ann. Probab., Tome 15 (1987) no. 4, pp. 40-74. http://gdmltest.u-ga.fr/item/1176992256/