Definition 4

The notations being those of Proposition 13, the diffusion $\Lambda H$ is called the composed diffusion (or the composition) of the bounded diffusions H and $\Lambda$.

Let $X_1, X_2, X_3, X_4$ be four locally compact spaces, and $\Lambda_1, \Lambda_2, \Lambda_3$ three bounded diffusions, of $X_1$ in $X_2$, $X_2$ in $X_3$, $X_3$ in $X_4$, respectively. It follows at once from Prop. 13 that

We will therefore use these notations without parentheses for the composition of diffusions.