John Armstrong (King’s College London)

Stochastic Differential Equations as Jets

We explain how Ito Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be used to derive graphical representations of Ito SDEs and how jets give rise to a coordinate free approach to understanding SDEs and diffusions on manifolds. We will consider some applications of this approach.