Institute of Mathematics for Industry

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Hypoelliptic SDE with jumps


Hold Date 2011-04-15 15:30~2011-04-15 17:00

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Hiroshi, KUNITA (emeritus professor at Kyushu University)

summary:
    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.