Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes

Alain Mazzolo, Cécile Monthus

For a diffusion process $X(t)$ of drift $\mu (x)$ and of diffusion coefficient $D=1/2$, we study the joint distribution of the two local times $A(t)={\int }_0^{t}d\tau \delta (X(\tau ))$ and $B(t…