论文标题
无限尺寸和SPDES的随机演算
Stochastic Calculus in Infinite Dimensions and SPDEs
论文作者
论文摘要
这些音符严格构建了由圆柱布朗尼运动驱动的希尔伯特空间的随机积分。我们扩展了这种随机演算，以介绍无限维度中随机微分方程的介绍，由于其物理重要性以及无绑定的噪声算子（并应用于运输噪声），因此特别关注Stratonovich方程。此外，我们探讨了非线性随机部分微分方程的存在理论中的技术。
These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to present an introduction to stochastic differential equations in infinite dimensions, with a particular focus on Stratonovich equations due to their physical importance as well as unbounded noise operators (with applications to transport noise). Furthermore we explore techniques in the existence theory for nonlinear stochastic partial differential equations.
