ABSTRACT
This chapter explores how stochastic differential equations can be naturally associated with linear partial differential equations via the expectations of functionals of the corresponding stochastic trajectories. A Feynman-Kac-type formula making the partial differential equations/stochastic differential equations connection are also given. In fact the new stochastic differential equation is not conventional and must be solved starting from the end, which explains the terminology backward: this is a standard case of a dynamic programming equation appearing in optimization problems, where repeated decisions/commands have to be applied over time.
