Multivariate regular variation of heavy-tailed Markov Chains
Multivariate regular variation of heavy-tailed Markov Chains
复制标题
重尾马尔可夫链的多元正则变体
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
J. Segers
中科院分区：
文献类型：
--
作者：
J. Segers
一般情况下，具有规则变化的平稳边际分布的马尔可夫链的上极值表现出一种称为尾链的乘法随机游动结构。更一般地，如果允许马尔可夫链从正极切换到负极或从负极切换到正极，则尾链增量的分布可能取决于前一步的尾链的符号。但即便如此，正向和向后的尾链也通过一种伴随关系相互决定。因此，马尔可夫链的有限维分布是以由来回尾链确定的方式规则地变化的多变量。该理论的应用给出了随机差分方程解的过去和未来的渐近分布，条件是现值的绝对值较大。
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is allowed to switch from positive to negative extremes or vice versa, the distribution of the tail chain increment may depend on the sign of the tail chain on the previous step. But even then, the forward and backward tail chain mutually determine each other through a kind of adjoint relation. As a consequence, the finite-dimensional distributions of the Markov chain are multivariate regularly varying in a way determined by the back-and-forth tail chain. An application of the theory yields the asymptotic distribution of the past and the future of the solution to a stochastic difference equation conditionally on the present value being large in absolute value.