论文标题
一类随机部分微分方程的大偏差原理，其完全局部单调系数受Lévy噪声的干扰
Large deviation principle for a class of stochastic partial differential equations with fully local monotone coefficients perturbed by Lévy noise
论文作者
论文摘要
在这项工作中，对一类带有局部单调系数的随机部分微分方程（SPDE）进行了渐近分析，这些系数涵盖了各种各样的物理系统，一类广泛的准线性SPD和大量流体动态模型。这项工作的目的是为上述SPDES的小高斯和泊松噪声扰动开发大偏差理论。我们建立了一个温柔的弗里德林型大偏差原理，用于使用lévy噪声在合适的波兰空间中扰动的强大解决方案，该SPD使用变异表示（基于弱收敛方法），用于对一般泊松随机测量和布朗尼的非阴性功能。相关的确定性控制问题的适合性是通过利用伪单调参数来确定的，随机对应物是通过应用Girsanov定理获得的。
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid dynamic models is carried out in this work. The aim of this work is to develop the large deviation theory for small Gaussian as well as Poisson noise perturbations of the above class of SPDEs. We establish a Wentzell-Freidlin type large deviation principle for the strong solutions to such SPDEs perturbed by Lévy noise in a suitable Polish space using a variational representation (based on a weak convergence approach) for nonnegative functionals of general Poisson random measures and Brownian motions. The well-posedness of an associated deterministic control problem is established by exploiting pseudo-monotonicity arguments and the stochastic counterpart is obtained by an application of Girsanov's theorem.
