A time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift \(\alpha (t)x+\beta (t)\) and linear infinitesimal variance 2r(t)x is considered. For this process, the transition density in the presence of an absorbing boundary in the zero-state and the first-passage time density through the zero-state are obtained. Special attention is dedicated to the proportional case, in which the immigration intensity function \(\beta (t)\) and the noise intensity function r(t) are connected via the relation \(\beta (t)=\xi \,r(t)\), with \(0\le \xi <1\). Various numerical computations are performed to illustrate the effect of the parameters on the first-passage time density, by assuming that \(\alpha (t)\), \(\beta (t)\) or both of these functions exhibit some kind of periodicity.

考虑了具有线性无穷小漂移\(\alpha (t)x+\beta (t)\)和线性无穷小方差 2 r ( t ) x的时间非均匀 Feller 型扩散过程。对于这个过程，获得了在零态存在吸收边界时的跃迁密度和通过零态的第一次通过时间密度。特别注意比例情况，其中移民强度函数\(\beta (t)\)和噪声强度函数r ( t ) 通过关系\(\beta (t)=\xi \, r(t)\) , 与\(0\le \xi <1\). 通过假设\(\alpha (t)\)、\(\beta (t)\)或这两个函数都表现出某种形式，进行了各种数值计算来说明参数对第一次通过时间密度的影响的周期性。