Deterministic Approach to Solving Stochastic PDEs
Abstract
Stochastic partial differential equations (SPDEs) form an interdisciplinary research area at the overlap of stochastic processes (random fields) and partial differential equations. Stochastic hydrodynamics, quantum physics, interacting particle systems, nonlinear filtering, and theory of super-processes have influenced the development of SPDEs at the overlap of stochastic processes (random fields) and partial differential equations. It is probably safe to say that in the last three decades the area of SPDEs has been one of the most dynamic areas of stochastic analysis. So far the theory and numerical methodology for stochastic PDEs or ODEs have dealt almost exclusively with Gaussian or Poisson/L«evy randomness. However, in various applications, practitioners are often forced to deal with a variety of types of random perturbations. The general goal of the research discussed in this proposal is the development of a sufficiently universal approach to solving linear and nonlinear stochastic PDEs driven by various types of random perturbations and their mixtures. More specifically, the proposal concentrates on stochastic PDEs with polynomial nonlinearity (e.g. stochastic Navier-Stokes, Burgers, etc). A substantial part of the proposal is concerned with the development of new methods for analysis and computations related to stochastic PDEs driven by arbitrary noise.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Dec 04, 2018
- Source ID
- W911NF1610103
Entities
People
- Boris Rozovsky
Organizations
- Army Contracting Command
- Brown University
- United States Army