Consider the affine random dynamical system $$ X_n = \mathbf A_n X_{n-1} + R_n, $$ where $\mathbf A_n\in\mathbb C^{d\times d}$ and $R_n\in\mathbb C^{d}$ with $R_n$ almost surely not equal to the zero vector. Is it possible to show that $$\lim_{n\to\infty}\frac{1}{n}\log||X_n|| \geq 0?$$
2026-04-29 13:08:14.1777468094
Linear affine random dynamical systems - positive lyapunov exponents?
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