论文标题
具有超线性增长系数的随机延迟微分方程的大偏差原理
Large deviations principle for stochastic delay differential equations with super-linearly growing coefficients
论文作者
论文摘要
我们利用弱收敛方法来建立Freidlin-Wentzell大偏差原理（LDP），用于具有超线性增长系数的随机延迟微分方程（SDDES），涵盖了具有非全球lipschitz系数的大量病例。我们证明中的关键要素是对受控方程的均匀力矩估计，在该方程中，我们通过迭代论点处理系数的超线性生长。我们的结果允许所考虑方程的漂移和扩散系数，不仅相对于延迟变量，而且在状态变量方面都可以增长。这项工作扩展了现有的结果，这些结果仅相对于延迟变量，它具有超线性增长系数的SDDES。
We utilize the weak convergence method to establish the Freidlin--Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases with non-globally Lipschitz coefficients. The key ingredient in our proof is the uniform moment estimate of the controlled equation, where we handle the super-linear growth of the coefficients by an iterative argument. Our results allow both the drift and diffusion coefficients of the considered equations to super-linearly grow not only with respect to the delay variable but also to the state variable. This work extends the existing results which develop the LDPs for SDDEs with super-linearly growing coefficients only with respect to the delay variable.
