# Infinitesimal generators of bridged stochastic process

 P: 13 Hi chiro The formal definition is the operator $\mathcal{L}$ where acts on $\mathcal{C}^{2, 1}$ test functions so that $\mathcal{L} f(x, t) = \lim_{h\rightarrow 0^+} \frac{\mathbb{E}(f(X_{t+h}) | X_t = x) - f(x)}{h}$. For general ito processes or levy processes it is easy to find, but for a bridged gamma process there is some trick I seem to be missing as I know you can do this in closed form.
 P: 523 The idea was to write the (conditional) transition density as $\frac{f(t,u,x,y)f(u,v,y,z)}{f(t,v,x,z)}$ and differentiate wrt u with the Kolmogorov equations. Does that help?