Transition probabilities in a problem of stochastic process switching

Extant solutions for state-contingent process switching use first-passage time densities or differential equations. We alternatively employ transition probabilities. These conditional likelihood functions also have obvious appeal for econometric analyses as well as derivative pricing and decision making under absorption and extinction.

► Transition probabilities for state-contingent absorption are derived. ► Transition densities and probabilities allow for the study of conditional likelihoods. ► Transition probabilities are central to maximum likelihood estimation. ► The results can be applied to various examples of absorption as well as extinction.