On the First-Passage Time Problem for a Feller-Type Diffusion Process

We consider the first-passage time problem for Feller-type diffusion process, having infinitesimal drift B1(x,t)=α(t)x+β(t) and variance B2(x,t)=2r(t)x, defined in space state [0,+∞), with α(t)∈R, β(t)>0, r(t)>0 continuous functions. For time-homogeneous case, some relations between densities of Feller process Wiener Ornstein–Uhlenbeck processes are discussed. The asymptotic behavior density through a time-dependent boundary is analyzed an asymptotically constant periodic boundary. Furthermore, when β(t)=ξr(t), ξ>0, we discuss obtain closed-form results special time-varying boundaries.