论文标题
有限相关时间各向同性随机系统的长期特性
Long-term properties of finite-correlation time isotropic stochastic systems
论文作者
论文摘要
我们考虑线性随机微分方程的有限维系统$ {\ partial_t} {x_k} \ left（t \ right）= {a_ {a_ {kp}} \ left（t \ right）{x_p} \ left（x_p}具有实际$ d \ times d $矩阵中的值。我们还假设$ {\ bf a}（t）$的法律满足大偏差原则。对于这些系统，我们找到了Lyapunov和广义Lyapunov指数的精确表达式，并表明它们仅由$ {\ bf a} $的对角线元素的速率函数以精确的方式确定。
We consider finite-dimensional systems of linear stochastic differential equations ${\partial_t}{x_k}\left( t \right) = {A_{kp}}\left( t \right){x_p}\left( t \right)$, ${\bf A}(t)$ being a stationary continuous statistically isotropic stochastic process with values in real $d \times d$ matrices. We suppose also that the laws of ${\bf A}(t)$ satisfy the large deviation principle. For these systems, we find exact expressions for the Lyapunov and generalized Lyapunov exponents and show that they are determined in a precise way only by the rate function of the diagonal elements of ${\bf A}$.
