An encounter-based approach for restricted diffusion with a gradient drift

We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards partially reactive boundary. For this purpose, we introduce extension of the Dirichlet-to-Neumann operator and use its eigenbasis to derive spectral decomposition full propagator, i.e., joint probability density function particle position boundary local time. This is central quantity that determines various characteristics diffusion-influenced reactions such as conventional propagators, survival probability, first-passage time distribution, reaction rate. As illustration, investigate impact constant onto on interval. More generally, accesses how external forces may influence statistics encounters diffusing