Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

The COMET-L3 experiment on long-term melt - concrete interaction and cooling by surface flooding

民族生态审美叙事的关键是科技隐喻与民族生态隐喻交合互动 ,它在正义性原则指导下可保证民族生存与文化具有可持续生存指标 ,一种吸收变革而不丧失认同性活力的能指 ,从而使人与自然及民族间的交往灵活地进行。进而 ,在科技隐喻与民族生态隐喻等“多重隐喻”的功能交合辐射的过程中 ,人类超越自身而形成把握实在意义的方式与前景 ,最终形成对科技导致的生态危机与民族冲突的超越