分野別セミナー

講演要旨：
We study SDE with jumps satisfying 'point-wise'
nondegenerate condition or 'point-wise' (modified)
Hormander's condition. We show that solutions of
these SDE have the hypoelliptic property described
below. The transition operator of the associated
jump-diffusion, weighted by a bounded smooth
function, can be extended from a smooth function
to a tempered distribution. The extended function
is a smooth function and satisfies Kolmogorov's
backward equation. As an application, we show that
the associated transition probablities have a smooth
density ans the density is the fundamental solution
of the asociated generator.
Our discussion is based on the Ｍａｌｌｉａｖｉｎ　
ｃａｌｃｕｌｕｓ on the Wiener-Poisson space.