Conditional Diffusion Models
摘要
We consider a one-dimensional diffusion process conditioned by hitting times. We call this process a\nconditional diffusion process. We obtain the generator of the conditional diffusion process. We compare\nthe original generator with that of the conditional diffusion process, and find a relation between these\ngenerators. By using this relation, we show some properties of the conditional diffusion process.\nOur results are applied to Bessel processes and diffusion models in population genetics. In population\ngenetics, the change of gene frequency is approximated by a one-dimensional diffusion process on [0,1].\nWe consider the diffusion model with random sampling drift and stochastic selection as the stochastic\nfactors of gene frequency change. For the case that the gene in question is surely lost from the population\n or fiexd in the population, some properties of the condition! diffusion processes in population genetics\nhave been studied. The end points are accessible in this case. Our results are applicable, however, to the\ncase that the end points are not necessary accessible.