Hypoellipticity of the Stochastic Partial Differential Operators.
Abstract
In different branches of science one often encounters the so-called stochastic partial differential equations, e.g., in quantum physics, transport theory, polymer physics, chemistry, signal detection, etc. These equations are then studied in the context of the particular situation from which they originate. This work aims to give a start for a systematic treatment of these equations. In fact, it begins with the ideal hypothesis: almost all of the operators are elliptic and the equations are driven on one hand with a drift term absolutely continuous with respect to the one dimensional Lebesgue measure and on the other hand, the diffusion term is given by a stochastic integral with respect to a finite dimensional Wiener process. This is typically the case encountered in the filtering of diffusion processes (cf. 2, 5, 10), except here the drift and diffusion operators are not respectively of the second and first order, they may depend on the whole history, and their coefficients are not necessarily semimartingales.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1985
- Accession Number
- ADA170326
Entities
People
- A. S. Ustunel
Organizations
- University of North Carolina at Chapel Hill