Time Homogeneous Processes with Given Marginal

John M. Noble (University of Warsaw)
Wednesday, November 12, 2014 - 6:00pm
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

In this talk, I consider the following problem: given a probability measure \mu over R with well defined expected value and given (deterministic) time, does there exist a gap diffusion with the prescribed law at the prescribed time?

This is answered in the affirmative and it is shown that, at least for an atomised space, that a diffusion satisfying the property may be approximated by solutions to fixed point problems.

The introduction of drift b and killing k is considered and conditions under which there is a function a such that a(1/2 + d^2/(dx^2) + b d/(dx) - k) is the infinitesimal generator of a process with the given marginal at the given prescribed time t > 0.