Saturday, November 4, 2006 - 3:45pm - 4:15pm
EE/CS 3-180
Erhan Cinlar (Princeton University)
For Hunt processes with jumps, we seek a treatment that concentrates
on the jumps. The idea is to use a generalized version of the renewal
theory (to which Blackwell was a seminal contributor). Embedded at
the jump times, there are Markov renewal processes (with continuous
state space) that decompose the original process into a sequence of
diffusions. Then, the original resolvent can be written as the
potential operator of a Markov chain acting on the resolvent of a
diffusion. Similar decompositions are possible for hitting
distributions and the transition semigroup. Theoretically, our
method reduces a jump diffusion to a combination of diffusions and
Markov chains.