2019/08/24 by Christian Kuehn, Kuehn, Christian, Alexandra Neamţu +1
Physics and Astronomy · Decision Sciences · Economics, Econometrics and Finance · #Advanced Thermodynamics and Statistical Mechanics #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1908.09177
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for SPDEs, which is always a challenge due to the irregularity of the noise terms that perturb the equation. In applications, such noise terms can quantify the lack of knowledge of certain parameters, finite-size effects, and/or fluctuations occurring due to external perturbations. Since SPDEs have become a key modelling tool in applications, there has been a growing interest in studying their dynamical phenomena. The main goal of this work is to provide a survey on different approaches to solution theory and dynamical properties for SPDEs, which is accessible for a wide community interested in modern methods in stochastic analysis, dynamics and applications.