Stochastic PDE
SPDEs including KPZ, stochastic Navier–Stokes, and Φ^4.
Stochastic PDE. SPDEs including KPZ, stochastic Navier–Stokes, and Φ^4.
Foundations and canonical references
The standard treatments of stochastic pde approach the subject from complementary angles. Daprato, Stochastic Equations in Infinite Dimensions (2014) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for stochastic pde include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2014Stochastic Equations in Infinite Dimensionsdaprato-2014, zabczyk-2014
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