Sticky Feller Diffusions

We consider a Feller branching diffusion process 𝑋 with drift 𝑐 having 0 as a slowly reflecting (sticky) boundary point with a stickiness parameter 1/𝜇 ∈ (0, ∞). We show that (i) the process 𝑋 can be characterised as a unique weak solution to the SDE system