Motivated by applications to stochastic differential equations, an extension of Hörmander’s hypoellipticity theorem is proved for second-order degenerate elliptic operators with non-smooth coefficients. The main results are established using point-wise Bessel kernel estimates and a weighted Sobolev inequality of Stein and Weiss. Of particular interest is that our results apply to operators with quite general first-order terms.
- Degenerate stochastic differential equations
- Hörmander’s theorem
- Malliavin calculus
- Pseudo-differential calculus
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