A Survey of Some Applications of Probability and Stochastic Control Theory to Finite Difference Methods for Degenerate Elliptic and Parabolic Equations.
Abstract
Finite difference methods for degenerate linear and (certain) non-linear elliptic and parabolic equations are analyzed from a probabilistic point of view, and probabilistic methods to show convergence to the correct weak or strong sense solution. The techniques generalize results in numerical analysis, and the probabilistic approach allows some additional physical insight to be brought to bear on the problem of selecting suitable approximations and methods of solution. The equations which are discussed all have probabilistic interpretations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1974
- Accession Number
- ADA002983
Entities
People
- Harold J. Kushner
Organizations
- Brown University