Hypoellipticity of the Stochastic Partial Differential Operators.
Technical rept. Sep 85-Aug 86,
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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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.
- Statistics and Probability