Functional central limit theorems and their associated large deviation principles for products of random matrices (Q1093237)

The main result of the paper concerns a uniformly mixing stationary sequence of random \(C^ 2\)-maps \(F_ k: [0,1]\to GL(d,{\mathbb{C}})\), \(k\geq 1\). It is shown that the law of the product \(Z^ a(t)=\prod^{[at]}_{k=1}F_ k(1/\sqrt{a})\) converges weakly as \(a\to \infty\) to a probability measure \({\mathbb{P}}\) on the space of continuous maps from [0,\(\infty)\) to GL(d,\({\mathbb{C}})\) which solves certain martingale problems. This theorem generalizes the result of \textit{M. A. Berger} [Trans. Am. Math. Soc. 285, 777-803 (1984; Zbl 0519.60012)]. The author derives also a large deviation principle for matrix solutions of linear stochastic differential equations in the Stratonovich form.