Bounds for the Mixing Rate in the Theory of Stochastic Equations
Bounds for the Mixing Rate in the Theory of Stochastic Equations
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DOI：
10.1137/1132036
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发表时间：
1988
影响因子：
0.6
通讯作者：
A. Veretennikov
中科院分区：
文献类型：
--
作者：
A. Veretennikov
1.导论.在某些混合系数减小得足够快的条件下，概率论的各种定理已被建立[1]-[3]。这个条件通常是混合系数的某个幂的收敛，也许是一个权函数。对于马尔可夫过程，[4]对一致强混合系数指数下降的条件作了深入的研究。然而，在许多情况下，比如说对于欧氏空间中的随机方程，这些条件并不满足，过程本身也不是一致强混合的。在这种情况下，可以希望估计较弱的混合系数。这是下文审查的情况。
1. Introduction. Various theorems of probabilitytheory have been established [1]-[3] under the condition that some mixing coefficient decreases fast enough. This condition is usually theconvergence of some power of the mixing coefficient, perhaps with a weight function. For Markov processes, a thorough study [4] has been made of conditions for the exponential decrease of the uniformly strong mixing coefficient. However, in a number ofsituations, say for stochastic equations in a Euclidean space, these conditions arenot satisfied and the processes themselves arenot uniformly strongly mixed. In such a case one can hope to estimate weaker mixing coefficients. This is the situation examined below.