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av J Sjöberg · Citerat av 39 — 2.6.2 Necessary Condition Using the HJB . . . .

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Locally , . “Hormander Condition for Delayed Diffusions” Abstract: In this talk we present some results that extends the Hormander condition to delayed diffusions. We will state a sufficient condition for the existence of density for the marginals of a delayed diffusion. This condition takes into account and quantifies the additional Some comments to the text by Lars H ormander: Fourier integral operators, Lectures at the Nordic Summer School in Mathematics, 1969.

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We furthermore say that the parabolic Hormander condition¨ holds at x if the Lie algebra generated by {∂ t +b}∪{σ j}m j=1 spans the whole tangent space of R×Td at (0,x).

bracket condition to fail on hypersurfaces in the domain of L. The theorem establishes the hupoellipticity of a large class of operators with points of infinite-type, and is sharp in the category of H¨ormander operators with smooth coefficients. In Section 4, we establish sufficient conditions for the existence of smooth densities W satisfies Hormander’s condition¨ (1) and the associated operator T K W is bounded from L 2(Rd) L2(Rd) !L1(Rd), but is unbounded from Lp1(Rd) Lp2(Rd) to Lp;¥(Rd) whenever 1 p1 + p 2 = p, 1 p 1;p 2 ¥ and p < 4 2d+3.
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Hormander condition

Subriemannian Hamiltonian function . In coordinates . Geodesic equation on : , in coordinates . is a geodesic and . Moreover we define the subriemannian geodesic flow .

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